Mayer, Daniel C.; Soullami, Abderazak Algebraic number fields generated by an infinite family of monogenic trinomials. (English) Zbl 1498.11215 Bol. Soc. Mat. Mex., III. Ser. 29, No. 1, Paper No. 1, 38 p. (2023). MSC: 11R04 11R16 11R20 11R21 11R27 11R29 11R37 11Y40 PDF BibTeX XML Cite \textit{D. C. Mayer} and \textit{A. Soullami}, Bol. Soc. Mat. Mex., III. Ser. 29, No. 1, Paper No. 1, 38 p. (2023; Zbl 1498.11215) Full Text: DOI arXiv OpenURL
Shahoseini, Ehsan; Rajaei, Ali; Maarefparvar, Abbas Ostrowski quotients for finite extensions of number fields. (English) Zbl 07666952 Pac. J. Math. 321, No. 2, 415-429 (2022). MSC: 11R29 11R37 11R34 11R21 PDF BibTeX XML Cite \textit{E. Shahoseini} et al., Pac. J. Math. 321, No. 2, 415--429 (2022; Zbl 07666952) Full Text: DOI arXiv OpenURL
Azizi, Abdelmalek; Chems-Eddin, Mohamed Mahmoud; Zekhnini, Abdelkader Note on the Hilbert 2-class field tower. (English) Zbl 07655824 Math. Bohem. 147, No. 4, 513-524 (2022). MSC: 11R11 11R16 11R20 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Math. Bohem. 147, No. 4, 513--524 (2022; Zbl 07655824) Full Text: DOI OpenURL
Gras, Georges On the \(\lambda\)-stability of \(p\)-class groups along cyclic \(p\)-towers of a number field. (English) Zbl 07572777 Int. J. Number Theory 18, No. 10, 2241-2263 (2022). MSC: 11R29 11R37 PDF BibTeX XML Cite \textit{G. Gras}, Int. J. Number Theory 18, No. 10, 2241--2263 (2022; Zbl 07572777) Full Text: DOI arXiv OpenURL
Azizi, Abdelmalek; Rezzougui, Mohammed; Zekhnini, Abdelkader Structure of the Galois group of the maximal unramified pro-2-extension of some \(\mathbb{Z}_2\)-extensions. (English) Zbl 1499.11335 Publ. Math. Debr. 100, No. 1-2, 11-28 (2022). Reviewer: Gabriel D. Villa Salvador (Ciudad de México) MSC: 11R23 20D15 11R11 11R20 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Publ. Math. Debr. 100, No. 1--2, 11--28 (2022; Zbl 1499.11335) Full Text: DOI OpenURL
Jaulent, Jean-François Abelian capitulation of ray class groups. (Capitulation abélienne des groupes de classes de rayons.) (French. English summary) Zbl 1485.11158 J. Number Theory 231, 316-332 (2022). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 11R29 11R23 PDF BibTeX XML Cite \textit{J.-F. Jaulent}, J. Number Theory 231, 316--332 (2022; Zbl 1485.11158) Full Text: DOI arXiv OpenURL
Aouissi, Siham; Talbi, Mohamed; Mayer, Daniel C.; Ismaili, Moulay Chrif 3-principalization over \(S_3\)-fields. (English) Zbl 1497.11275 Turk. J. Math. 45, No. 5, 2225-2247 (2021). MSC: 11R37 11R29 11R32 11R20 11R16 20D15 20F05 PDF BibTeX XML Cite \textit{S. Aouissi} et al., Turk. J. Math. 45, No. 5, 2225--2247 (2021; Zbl 1497.11275) Full Text: DOI arXiv OpenURL
Wang, Weitong; Wood, Melanie Matchett Moments and interpretations of the Cohen-Lenstra-Martinet heuristics. (English) Zbl 1472.11284 Comment. Math. Helv. 96, No. 2, 339-387 (2021). MSC: 11R29 11R32 11R45 PDF BibTeX XML Cite \textit{W. Wang} and \textit{M. M. Wood}, Comment. Math. Helv. 96, No. 2, 339--387 (2021; Zbl 1472.11284) Full Text: DOI arXiv OpenURL
Chems-Eddin, Mohamed Mahmoud; Azizi, Abdelmalek; Zekhnini, Abdelkader; Jerrari, Idriss On the Hilbert \(2\)-class field tower of some imaginary biquadratic number fields. (English) Zbl 07332716 Czech. Math. J. 71, No. 1, 269-281 (2021). MSC: 11R11 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{M. M. Chems-Eddin} et al., Czech. Math. J. 71, No. 1, 269--281 (2021; Zbl 07332716) Full Text: DOI OpenURL
Lai, King Fai; Tan, Ki-Seng A generalized Iwasawa’s theorem and its application. (English) Zbl 1472.11283 Res. Math. Sci. 8, No. 2, Paper No. 20, 18 p. (2021). Reviewer: Andrea Bandini (Pisa) MSC: 11R29 11R23 12G05 11R65 PDF BibTeX XML Cite \textit{K. F. Lai} and \textit{K.-S. Tan}, Res. Math. Sci. 8, No. 2, Paper No. 20, 18 p. (2021; Zbl 1472.11283) Full Text: DOI OpenURL
Caldarola, Fabio On the maximal finite Iwasawa submodule in \(\mathbb{Z}_p\)-extensions and capitulation of ideals. (English) Zbl 1470.11277 Rend. Semin. Mat., Univ. Politec. Torino 78, No. 1, 27-42 (2020). Reviewer: Andreas Nickel (Essen) MSC: 11R23 11R29 PDF BibTeX XML Cite \textit{F. Caldarola}, Rend. Semin. Mat., Univ. Politec. Torino 78, No. 1, 27--42 (2020; Zbl 1470.11277) Full Text: Link OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader The structure of the second \(2\)-class group of some special Dirichlet fields. (English) Zbl 1442.11154 Asian-Eur. J. Math. 13, No. 3, Article ID 2050053, 6 p. (2020). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R37 11R11 11R20 11R29 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{A. Zekhnini}, Asian-Eur. J. Math. 13, No. 3, Article ID 2050053, 6 p. (2020; Zbl 1442.11154) Full Text: DOI OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed On the capitulation of the 2-ideal classes of the field \(\mathbb{Q}(\sqrt{p_1p_2q},i)\) of type \((2,2,2)\). (English) Zbl 1431.11118 Bol. Soc. Parana. Mat. (3) 38, No. 4, 127-135 (2020). MSC: 11R11 11R16 11R20 11R27 11R29 PDF BibTeX XML Cite \textit{A. Azizi} et al., Bol. Soc. Parana. Mat. (3) 38, No. 4, 127--135 (2020; Zbl 1431.11118) Full Text: Link OpenURL
González-Avilés, Cristian D. Čech cohomology and the capitulation kernel. (English) Zbl 1436.11137 Funct. Approximatio, Comment. Math. 61, No. 1, 95-108 (2019). MSC: 11R34 11R27 14F20 PDF BibTeX XML Cite \textit{C. D. González-Avilés}, Funct. Approximatio, Comment. Math. 61, No. 1, 95--108 (2019; Zbl 1436.11137) Full Text: DOI arXiv Euclid OpenURL
Azizi, Abdelmalek; Jerrari, Idriss; Zekhnini, Abdelkader; Talbi, Mohammed On the 2-class field towers of some imaginary quartic cyclic number fields. (English) Zbl 1454.11198 Colloq. Math. 158, No. 1, 103-118 (2019). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R11 11R16 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Colloq. Math. 158, No. 1, 103--118 (2019; Zbl 1454.11198) Full Text: DOI OpenURL
Agathocleous, Eleni The 3-part of the ideal class group of a certain family of real cyclotomic fields. (English) Zbl 1452.11131 Acta Arith. 190, No. 3, 305-315 (2019). MSC: 11R29 11R18 11R80 11Y40 PDF BibTeX XML Cite \textit{E. Agathocleous}, Acta Arith. 190, No. 3, 305--315 (2019; Zbl 1452.11131) Full Text: DOI arXiv OpenURL
González-Avilés, Cristian D. The norm map and the capitulation kernel. (English) Zbl 1459.11216 J. Number Theory 202, 388-411 (2019). MSC: 11R29 14F20 PDF BibTeX XML Cite \textit{C. D. González-Avilés}, J. Number Theory 202, 388--411 (2019; Zbl 1459.11216) Full Text: DOI arXiv OpenURL
Mouhib, Ali Application of Greenberg’s conjecture in the capitulation problem. (English) Zbl 1437.11151 Math. Nachr. 292, No. 3, 633-639 (2019). MSC: 11R23 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Mouhib}, Math. Nachr. 292, No. 3, 633--639 (2019; Zbl 1437.11151) Full Text: DOI OpenURL
Azizi, A.; Jerrari, I.; Talbi, M. On the rank of the 2-class group of an extension of degree 8 over \(\mathbb{Q}\). (English) Zbl 1438.11136 Period. Math. Hung. 78, No. 1, 128-134 (2019). Reviewer: Gabriel D. Villa Salvador (Ciudad de México) MSC: 11R16 11R11 11R29 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Period. Math. Hung. 78, No. 1, 128--134 (2019; Zbl 1438.11136) Full Text: DOI OpenURL
Azizi, Abdelmalek; Jerrari, Idriss; Zekhnini, Abdelkader; Talbi, Mohammed Capitulation of the 2-ideal classes of type \((2, 2, 2)\) of some quartic cyclic number fields. (English) Zbl 1415.11150 J. Math. Cryptol. 13, No. 1, 27-46 (2019). MSC: 11R16 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., J. Math. Cryptol. 13, No. 1, 27--46 (2019; Zbl 1415.11150) Full Text: DOI OpenURL
Mouhib, Ali On the 2-class field tower of subfields of some cyclotomic \(\mathbb {Z}_2\)-extensions. (English) Zbl 1498.11221 Math. Slovaca 69, No. 1, 81-86 (2019). MSC: 11R29 11R37 11R23 11R32 PDF BibTeX XML Cite \textit{A. Mouhib}, Math. Slovaca 69, No. 1, 81--86 (2019; Zbl 1498.11221) Full Text: DOI OpenURL
Bond, Robert J. Capitulation in abelian extensions of number fields. (English) Zbl 1385.11071 Acta Arith. 179, No. 3, 201-232 (2017). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 11R34 PDF BibTeX XML Cite \textit{R. J. Bond}, Acta Arith. 179, No. 3, 201--232 (2017; Zbl 1385.11071) Full Text: DOI OpenURL
Nguyen Quang Do, Thong Galois descent and capitulation between Bertrandias-Payan modules. (Descente Galoisienne et capitulation entre modules de Bertrandias-Payan.) (French. English summary) Zbl 1380.11093 Algèbre et théorie des nombres 2016. Besançon: Presses Universitaires de Franche-Comté. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2016, 59-79 (2017). Reviewer: Andrea Bandini (Parma) MSC: 11R37 11R34 11R23 PDF BibTeX XML Cite \textit{T. Nguyen Quang Do}, Publ. Math. Besançon, Algèbre Théor. Nombres 2016, 59--79 (2017; Zbl 1380.11093) Full Text: Link OpenURL
Jaulent, Jean-François On the capitulation for the Bertrandias-Payan module. (Sur la capitulation pour le module de Bertrandias-Payan.) (French. English summary) Zbl 1406.11113 Algèbre et théorie des nombres 2016. Besançon: Presses Universitaires de Franche-Comté. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2016, 45-58 (2017). MSC: 11R37 11R23 PDF BibTeX XML Cite \textit{J.-F. Jaulent}, Publ. Math. Besançon, Algèbre Théor. Nombres 2016, 45--58 (2017; Zbl 1406.11113) Full Text: arXiv OpenURL
Gras, Georges On the Bertrandias-Payan module in a \(p\)-extension – capitulation kernel. (Sur le module de Bertrandias-Payan dans une \(p\)-extension – Noyau de capitulation.) (French. English summary) Zbl 1406.11112 Algèbre et théorie des nombres 2016. Besançon: Presses Universitaires de Franche-Comté. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2016, 25-44 (2017). MSC: 11R37 11R04 PDF BibTeX XML Cite \textit{G. Gras}, Publ. Math. Besançon, Algèbre Théor. Nombres 2016, 25--44 (2017; Zbl 1406.11112) Full Text: arXiv OpenURL
Azizi, A.; Jerrari, I.; Zekhnini, A.; Talbi, M. On the second 2-class group \(\mathrm{Gal}(K_2^{(2)} / K)\) of some imaginary quartic cyclic number field \(K\). (English) Zbl 1428.11190 J. Number Theory 177, 562-588 (2017). MSC: 11R16 11R11 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., J. Number Theory 177, 562--588 (2017; Zbl 1428.11190) Full Text: DOI OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed Capitulation in the absolutely abelian extensions of some number fields. II. (English) Zbl 1422.11228 Acta Math. Vietnam. 42, No. 1, 81-97 (2017). MSC: 11R37 11R11 11R16 11R20 11R27 11R29 PDF BibTeX XML Cite \textit{A. Azizi} et al., Acta Math. Vietnam. 42, No. 1, 81--97 (2017; Zbl 1422.11228) Full Text: DOI arXiv OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed On some metabelian 2-group and applications. II. (English) Zbl 1415.11169 Bol. Soc. Parana. Mat. (3) 34, No. 2, 75-85 (2016). MSC: 11R37 11R11 11R29 11R32 PDF BibTeX XML Cite \textit{A. Azizi} et al., Bol. Soc. Parana. Mat. (3) 34, No. 2, 75--85 (2016; Zbl 1415.11169) Full Text: Link OpenURL
Jaulent, Jean-François Logarithmic classes and capitulation. (Classes logarithmiques et capitulation.) (French. English summary) Zbl 1404.11129 Funct. Approximatio, Comment. Math. 54, No. 2, 227-239 (2016). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 11R29 11R32 PDF BibTeX XML Cite \textit{J.-F. Jaulent}, Funct. Approximatio, Comment. Math. 54, No. 2, 227--239 (2016; Zbl 1404.11129) Full Text: DOI arXiv Euclid OpenURL
Mouhib, Ali A remark on the capitulation problem. (English) Zbl 1389.11138 Period. Math. Hung. 73, No. 1, 120-129 (2016). Reviewer: Günter Lettl (Graz) MSC: 11R29 11R32 11R37 11R23 PDF BibTeX XML Cite \textit{A. Mouhib}, Period. Math. Hung. 73, No. 1, 120--129 (2016; Zbl 1389.11138) Full Text: DOI OpenURL
Azizi, Abdelmalek; Taous, Mohammed; Zekhnini, Abdelkader On the \(2\)-groups whose abelianizations are of type \((2, 4)\) and applications. (English) Zbl 1389.11133 Publ. Math. Debr. 88, No. 1-2, 93-117 (2016). Reviewer: Nikolai L. Manev (Sofia) MSC: 11R11 11R29 11R32 11R37 20F05 PDF BibTeX XML Cite \textit{A. Azizi} et al., Publ. Math. Debr. 88, No. 1--2, 93--117 (2016; Zbl 1389.11133) Full Text: DOI OpenURL
Caldarola, Fabio Invariants and coinvariants of class groups in \({\mathbb Z}_p\)-extensions and Greenberg’s conjecture. (English) Zbl 1411.11104 Riv. Mat. Univ. Parma (N.S.) 7, No. 1, 181-192 (2016). MSC: 11R23 11R29 PDF BibTeX XML Cite \textit{F. Caldarola}, Riv. Mat. Univ. Parma (N.S.) 7, No. 1, 181--192 (2016; Zbl 1411.11104) OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed Group theory and the capitulation problem for some number fields. (English) Zbl 1417.11151 Gueye, Cheikh Thiécoumbe (ed.) et al., Non-associative and non-commutative algebra and operator theory. NANCAOT, Dakar, Senegal, May 23–25, 2014: workshop in honor of Professor Amin Kaidi. Cham: Springer. Springer Proc. Math. Stat. 160, 3-26 (2016). MSC: 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Springer Proc. Math. Stat. 160, 3--26 (2016; Zbl 1417.11151) Full Text: DOI OpenURL
Azizi, Abdelmalek; Jerrari, Idriss; Talbi, Mohammed The capitulation problem for certain cyclic quartic number fields. (English) Zbl 1381.11104 Tokyo J. Math. 39, No. 2, 351-359 (2016). Reviewer: Claude Levesque (Québec) MSC: 11R27 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Tokyo J. Math. 39, No. 2, 351--359 (2016; Zbl 1381.11104) Full Text: DOI Euclid OpenURL
Zekhnini, Abdelkader Imaginary biquadratic Polya fields of the form \(Q(\sqrt d,\sqrt{-2})\). (English) Zbl 1405.11143 Gulf J. Math. 4, No. 4, 182-188 (2016). MSC: 11R16 11R29 13F20 PDF BibTeX XML Cite \textit{A. Zekhnini}, Gulf J. Math. 4, No. 4, 182--188 (2016; Zbl 1405.11143) OpenURL
Mayer, Daniel C. Recent progress in determining \(p\)-class field towers. (English) Zbl 1401.11147 Gulf J. Math. 4, No. 4, 74-102 (2016). MSC: 11R37 11R29 12F10 PDF BibTeX XML Cite \textit{D. C. Mayer}, Gulf J. Math. 4, No. 4, 74--102 (2016; Zbl 1401.11147) Full Text: arXiv OpenURL
Bandini, Andrea; Caldarola, Fabio Stabilization for Iwasawa modules in \(\mathbb{Z}_p\)-extensions. (English) Zbl 1368.11114 Rend. Semin. Mat. Univ. Padova 136, 137-155 (2016). Reviewer: Andreas Nickel (Essen) MSC: 11R23 11R29 PDF BibTeX XML Cite \textit{A. Bandini} and \textit{F. Caldarola}, Rend. Semin. Mat. Univ. Padova 136, 137--155 (2016; Zbl 1368.11114) Full Text: DOI OpenURL
Zekhnini, Abdelkader; Azizi, Abdelmalek; Taous, Mohammed On some metabelian 2-groups and applications. III. (English) Zbl 1400.11137 Asian-Eur. J. Math. 9, No. 4, Article ID 1650072, 11 p. (2016). MSC: 11R11 11R29 11R32 11R37 20D15 PDF BibTeX XML Cite \textit{A. Zekhnini} et al., Asian-Eur. J. Math. 9, No. 4, Article ID 1650072, 11 p. (2016; Zbl 1400.11137) Full Text: DOI OpenURL
Mouhib, Ali Capitulation of the 2-class group of some cyclic number fields with large degree. (English) Zbl 1401.11148 Math. Nachr. 289, No. 14-15, 1927-1933 (2016). MSC: 11R37 11R23 11R29 11R32 PDF BibTeX XML Cite \textit{A. Mouhib}, Math. Nachr. 289, No. 14--15, 1927--1933 (2016; Zbl 1401.11148) Full Text: DOI OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed On the strongly ambiguous classes of some biquadratic number fields. (English) Zbl 1413.11120 Math. Bohem. 141, No. 3, 363-384 (2016). Reviewer: Elliot Benjamin (Winterport) MSC: 11R11 11R16 11R20 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Math. Bohem. 141, No. 3, 363--384 (2016; Zbl 1413.11120) Full Text: DOI arXiv OpenURL
Ji, Feng Weyl groups, ideal class groups and the \(K\)-theory of the extension functor. (English) Zbl 1401.11144 Commun. Algebra 44, No. 3, 1200-1226 (2016). MSC: 11R29 19D55 PDF BibTeX XML Cite \textit{F. Ji}, Commun. Algebra 44, No. 3, 1200--1226 (2016; Zbl 1401.11144) Full Text: DOI OpenURL
Folk, David Making sense of capitulation: reciprocal primes. (English) Zbl 1354.11070 Acta Arith. 172, No. 4, 325-332 (2016). Reviewer: Alessandro Cobbe (Neubiberg) MSC: 11R37 11R29 PDF BibTeX XML Cite \textit{D. Folk}, Acta Arith. 172, No. 4, 325--332 (2016; Zbl 1354.11070) Full Text: DOI OpenURL
Mayer, Daniel C. New number fields with known \(p\)-class tower. (English) Zbl 1392.11086 Tatra Mt. Math. Publ. 64, 21-57 (2015). MSC: 11R37 11R29 11R11 11R16 PDF BibTeX XML Cite \textit{D. C. Mayer}, Tatra Mt. Math. Publ. 64, 21--57 (2015; Zbl 1392.11086) Full Text: DOI arXiv OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed; Mayer, Daniel C. Principalization of 2-class groups of type (2, 2, 2) of biquadratic fields \(\mathbb{Q}(\sqrt{p_1p_2q},\sqrt{-1})\). (English) Zbl 1319.11079 Int. J. Number Theory 11, No. 4, 1177-1215 (2015). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R37 11R16 11R29 11R32 PDF BibTeX XML Cite \textit{A. Azizi} et al., Int. J. Number Theory 11, No. 4, 1177--1215 (2015; Zbl 1319.11079) Full Text: DOI arXiv OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed Structure of \(\mathrm {Gal}(\Bbbk _2^{(2)}/\Bbbk)\) for some fields \(\Bbbk=\mathbb {Q}(\sqrt{2p_1p_2},i)\) with \(\mathbf {C}l_2(\Bbbk)\simeq (2, 2, 2)\). (English) Zbl 1361.11063 Abh. Math. Semin. Univ. Hamb. 84, No. 2, 203-231 (2014). MSC: 11R11 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Abh. Math. Semin. Univ. Hamb. 84, No. 2, 203--231 (2014; Zbl 1361.11063) Full Text: DOI arXiv OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed On a capitulation problem over the field \(\mathbb {Q}(\sqrt {p_1p_2},\text{i})\) with elementary \(2\)-class group. (Sur un problème de capitulation du corps \(\mathbb {Q}(\sqrt {p_1p_2},\text{i})\) dont le \(2\)-groupe de classes est élémentaire.) (French. English summary) Zbl 1340.11088 Czech. Math. J. 64, No. 1, 11-29 (2014). Reviewer: Roland Quême (Brax) MSC: 11R29 11R37 11R27 PDF BibTeX XML Cite \textit{A. Azizi} et al., Czech. Math. J. 64, No. 1, 11--29 (2014; Zbl 1340.11088) Full Text: DOI OpenURL
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed On the strongly ambiguous classes of \(k/\mathbb Q(i)\) where \(k=\mathbb Q(\sqrt{2p_1p_2}, i)\). (English) Zbl 1292.11119 Asian-Eur. J. Math. 7, No. 1, Article ID 1450021, 26 p. (2014). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R11 11R16 11R20 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Asian-Eur. J. Math. 7, No. 1, Article ID 1450021, 26 p. (2014; Zbl 1292.11119) Full Text: DOI arXiv OpenURL
Azizi, Abdelmalek; Rezzougui, Mohammed 2-class fields towers of some imaginary biquadratic number fields. (English) Zbl 1392.11085 Int. Electron. J. Pure Appl. Math. 6, No. 3, 127-132 (2013). MSC: 11R27 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{M. Rezzougui}, Int. Electron. J. Pure Appl. Math. 6, No. 3, 127--132 (2013; Zbl 1392.11085) Full Text: DOI Link OpenURL
Azizi, Abdelmalek; Talbi, Mohammed On a question of capitulation. (Sur une question de capitulation.) (French) Zbl 1378.11093 Acta Math. Vietnam. 38, No. 2, 207-212 (2013). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{M. Talbi}, Acta Math. Vietnam. 38, No. 2, 207--212 (2013; Zbl 1378.11093) Full Text: DOI OpenURL
Bembom, Tobias The capitulation problem in class field theory. (English) Zbl 1298.11104 Göttingen: Univ. Göttingen (Diss.). 157 p. (2012). MSC: 11R37 11R34 11-02 PDF BibTeX XML Cite \textit{T. Bembom}, The capitulation problem in class field theory. Göttingen: Univ. Göttingen (Diss.) (2012; Zbl 1298.11104) Full Text: arXiv Link OpenURL
Azizi, Abdelmalek; Talbi, Mohammed Galois group of certain class fields. (Groupe de Galois de certains corps de classes.) (French. English summary) Zbl 1274.11164 An. Științ. Univ. “Ovidius” Constanța, Ser. Mat. 19, No. 3, 27-50 (2011). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R27 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{M. Talbi}, An. Științ. Univ. ``Ovidius'' Constanța, Ser. Mat. 19, No. 3, 27--50 (2011; Zbl 1274.11164) OpenURL
Li, Yan; Hu, Su Capitulation problem for global function fields. (English) Zbl 1281.11097 Arch. Math. 97, No. 5, 413-421 (2011). MSC: 11R58 11A15 11R37 PDF BibTeX XML Cite \textit{Y. Li} and \textit{S. Hu}, Arch. Math. 97, No. 5, 413--421 (2011; Zbl 1281.11097) Full Text: DOI OpenURL
Pitoun, Frédéric Capitulation’s cokernel and Iwasawa modules. (Conoyaux de capitulation et modules d’Iwasawa.) (French. English summary) Zbl 1234.11151 Int. J. Number Theory 7, No. 6, 1503-1517 (2011). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11R23 PDF BibTeX XML Cite \textit{F. Pitoun}, Int. J. Number Theory 7, No. 6, 1503--1517 (2011; Zbl 1234.11151) Full Text: DOI OpenURL
Gruenberg, K. W.; Weiss, A. Transfer kernels for finite groups. II. (English) Zbl 1228.20007 J. Algebra 326, No. 1, 122-129 (2011). Reviewer: Olympia Talelli (Athens) MSC: 20C10 20J06 20D15 PDF BibTeX XML Cite \textit{K. W. Gruenberg} and \textit{A. Weiss}, J. Algebra 326, No. 1, 122--129 (2011; Zbl 1228.20007) Full Text: DOI OpenURL
Azizi, Abdelmalek; Talbi, Mohammed Structure of Galois group for certain class fields. (Structure du groupe de Galois pour certains corps de classes.) (French) Zbl 1246.11170 Int. J. Algebra 4, No. 21-24, 1127-1136 (2010). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R16 11R37 11R27 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{M. Talbi}, Int. J. Algebra 4, No. 21--24, 1127--1136 (2010; Zbl 1246.11170) Full Text: Link OpenURL
González-Avilés, Cristian D. On Néron-Raynaud class groups of tori and the capitulation problem. (English) Zbl 1230.11137 J. Reine Angew. Math. 648, 149-182 (2010). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11R29 11R34 PDF BibTeX XML Cite \textit{C. D. González-Avilés}, J. Reine Angew. Math. 648, 149--182 (2010; Zbl 1230.11137) Full Text: DOI arXiv OpenURL
Schoof, René; Washington, Lawrence C. Visibility of ideal classes. (English) Zbl 1226.11123 J. Number Theory 130, No. 12, 2715-2731 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11R37 11R18 11R33 11R34 PDF BibTeX XML Cite \textit{R. Schoof} and \textit{L. C. Washington}, J. Number Theory 130, No. 12, 2715--2731 (2010; Zbl 1226.11123) Full Text: DOI arXiv OpenURL
Bosca, Sébastien [Gras, Georges; Jaulent, Jean-François] Principalization of ideals in abelian extensions of number fields. With an appendix by Georges Gras and Jean-François Jaulent. (English) Zbl 1239.11118 Int. J. Number Theory 5, No. 3, 527-539 (2009). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R20 11R37 11R45 PDF BibTeX XML Cite \textit{S. Bosca}, Int. J. Number Theory 5, No. 3, 527--539 (2009; Zbl 1239.11118) Full Text: DOI OpenURL
Greither, Cornelius; Johnston, Henri Capitulation for locally free class groups of orders of group algebras over number fields. (English) Zbl 1189.11052 Bull. Lond. Math. Soc. 41, No. 3, 541-548 (2009). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R33 11R65 PDF BibTeX XML Cite \textit{C. Greither} and \textit{H. Johnston}, Bull. Lond. Math. Soc. 41, No. 3, 541--548 (2009; Zbl 1189.11052) Full Text: DOI arXiv OpenURL
Asghari-Larimi, Mohsen; Movahhedi, Abbas Bounds for étale capitulation kernels. II. (Bornes pour les noyaux de capitulations. II.) (English) Zbl 1171.11059 Ann. Math. Blaise Pascal 16, No. 1, 151-163 (2009). Reviewer: Kevin Hutchinson (Dublin) MSC: 11R70 19F27 PDF BibTeX XML Cite \textit{M. Asghari-Larimi} and \textit{A. Movahhedi}, Ann. Math. Blaise Pascal 16, No. 1, 151--163 (2009; Zbl 1171.11059) Full Text: DOI Numdam EuDML OpenURL
Azizi, Abdelmalek; Talbi, Mohammed Capitulation of 2-class ideals of \(\mathbb Q\left(\sqrt{-pq(2+\sqrt 2)}\right)\) where \(p\equiv q\equiv {\pm 5} \bmod 8\). (Capitulation des 2-classes d’idéaux de \(\mathbb Q \left(\sqrt{-pq(2+\sqrt 2)}\right)\) où \(p\equiv q\equiv {\pm 5} \bmod 8\).) (French) Zbl 1169.11046 Ann. Math. Blaise Pascal 16, No. 1, 57-69 (2009). Reviewer: Paul Buckingham (Edmonton) MSC: 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{M. Talbi}, Ann. Math. Blaise Pascal 16, No. 1, 57--69 (2009; Zbl 1169.11046) Full Text: DOI Numdam EuDML OpenURL
Azizi, Abdelmalek; Talbi, M. Capitulation in certain unramified extensions of cyclic quartic fields. (Capitulation dans certaines extensions non ramifiées de corps quartiques cycliques.) (French) Zbl 1212.11091 Arch. Math., Brno 44, No. 4, 271-284 (2008). MSC: 11R27 11R37 11R16 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{M. Talbi}, Arch. Math., Brno 44, No. 4, 271--284 (2008; Zbl 1212.11091) Full Text: EuDML EMIS OpenURL
Vauclair, David Tate kernels and capitulation. (Noyaux de Tate et capitulation.) (French) Zbl 1194.11101 J. Number Theory 128, No. 3, 619-638 (2008). Reviewer: Sunil K. Chebolu (Normal, IL) MSC: 11R23 11R34 11R70 PDF BibTeX XML Cite \textit{D. Vauclair}, J. Number Theory 128, No. 3, 619--638 (2008; Zbl 1194.11101) Full Text: DOI OpenURL
Azizi, Abdelmalek; Taous, Mohammed Capitulation of the 2-class group of \({\mathbf k} = {\mathbb Q}(\sqrt{2p},i)\). (Capitulation des 2-classes d’idéaux de \({\mathbf k} = {\mathbb Q}(\sqrt{2p},i)\).) (French) Zbl 1139.11048 Acta Arith. 131, No. 2, 103-123 (2008). Reviewer: Florin Nicolae (Berlin) MSC: 11R37 11R29 11R27 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{M. Taous}, Acta Arith. 131, No. 2, 103--123 (2008; Zbl 1139.11048) Full Text: DOI arXiv OpenURL
Azizi, Abdelmalek; Taous, Mohammed Capitulation of 2-ideal classes of \(k=\mathbb Q(\sqrt{2p},i)\) in the genus field of \(k\) where \(p\) is prime such that \(p\equiv 1 \bmod 8\). (English) Zbl 1169.11047 Int. J. Pure Appl. Math. 35, No. 4, 481-487 (2007). Reviewer: Paul Buckingham (Edmonton) MSC: 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{M. Taous}, Int. J. Pure Appl. Math. 35, No. 4, 481--487 (2007; Zbl 1169.11047) OpenURL
Son, Jung-Je; Kwon, Soun-Hi On the principal ideal theorem. (English) Zbl 1126.11065 J. Korean Math. Soc. 44, No. 4, 747-756 (2007). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 11R29 11R11 11Y40 PDF BibTeX XML Cite \textit{J.-J. Son} and \textit{S.-H. Kwon}, J. Korean Math. Soc. 44, No. 4, 747--756 (2007; Zbl 1126.11065) Full Text: DOI OpenURL
Vauclair, David On the comparison of higher order Tate kernels. (Sur la comparaison des noyaux de Tate d’ordre supérieur.) (French) Zbl 1221.11216 Algèbre et théorie des nombres. Années 2003–2006. Besançon: Laboratoire de Mathématiques de Besançon. Publications Mathématiques de l’Université de Franche-Comté Besançon. Algèbre et Théorie des Nombres 2003-2006, 117-127 (2006). Reviewer: Florin Nicolae (Berlin) MSC: 11R23 11R34 11R37 PDF BibTeX XML Cite \textit{D. Vauclair}, in: Algèbre et théorie des nombres. Années 2003--2006. Besançon: Laboratoire de Mathématiques de Besançon. 117--127 (2006; Zbl 1221.11216) OpenURL
Fuluta, Kazuyuki On capitulation theorems for infinite groups. (English) Zbl 1146.55010 Kohno, Toshitake (ed.) et al., Primes and knots. Proceedings of an AMS special session, Baltimore, MD, USA, January 15–16, 2003 and the 15th JAMI (Japan-US Mathematics Institute) conference, Baltimore, MD, USA, March 7–16, 2003. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3456-8/pbk). Contemporary Mathematics 416, 41-47 (2006). MSC: 55R12 20E36 57M12 PDF BibTeX XML Cite \textit{K. Fuluta}, Contemp. Math. 416, 41--47 (2006; Zbl 1146.55010) OpenURL
Benjamin, Elliot On the 2-class field tower of some imaginary biquadratic number fields. (English) Zbl 1161.11401 Ramanujan J. 11, No. 1, 103-110 (2006). MSC: 11R37 11R29 11R11 11R16 PDF BibTeX XML Cite \textit{E. Benjamin}, Ramanujan J. 11, No. 1, 103--110 (2006; Zbl 1161.11401) Full Text: DOI OpenURL
Gruenberg, K. W.; Weiss, A. Transfer kernels for finite groups. (English) Zbl 1111.20011 J. Algebra 300, No. 1, 35-43 (2006). Reviewer: Kanat Abdukhalikov (Fukuoka) MSC: 20C10 20J06 20D15 PDF BibTeX XML Cite \textit{K. W. Gruenberg} and \textit{A. Weiss}, J. Algebra 300, No. 1, 35--43 (2006; Zbl 1111.20011) Full Text: DOI OpenURL
Azizi, Abdelmalek; Benhamza, Ikram On the capitulation of 2-ideal classes of \(\mathbb Q(\sqrt{d},\sqrt{-2})\). (Sur la capitulation des 2-classes d’idéaux de \(\mathbb Q(\sqrt{d},\sqrt{-2})\).) (French. English summary) Zbl 1217.11097 Ann. Sci. Math. Qué. 29, No. 1, 1-20 (2005). MSC: 11R29 11R16 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{I. Benhamza}, Ann. Sci. Math. Qué. 29, No. 1, 1--20 (2005; Zbl 1217.11097) Full Text: Link OpenURL
Vauclair, David Cup product, étale capitulation kernels and generalized Greenberg conjecture. (Cup-produit, noyaux de capitulation étales et conjecture de Greenberg généralisée.) (French) Zbl 1156.11342 \(K\)-Theory 36, No. 3-4, 223-244 (2005). MSC: 11R70 11R23 11R34 PDF BibTeX XML Cite \textit{D. Vauclair}, \(K\)-Theory 36, No. 3--4, 223--244 (2005; Zbl 1156.11342) Full Text: DOI OpenURL
Nguyen Quang Do, Thong; Vauclair, David \(K_2\) and the Greenberg conjecture in multiple \(\mathbb Z_p\)-extensions. (\(K_2\) et conjecture de Greenberg dans les \(\mathbb Z_p\)-extensions multiples.) (French) Zbl 1091.11041 J. Théor. Nombres Bordx. 17, No. 2, 669-688 (2005). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R70 11R33 11R23 PDF BibTeX XML Cite \textit{T. Nguyen Quang Do} and \textit{D. Vauclair}, J. Théor. Nombres Bordx. 17, No. 2, 669--688 (2005; Zbl 1091.11041) Full Text: DOI Numdam EuDML OpenURL
Le Floc’h, M.; Movahhedi, A.; Nguyen Quang Do, T. On capitulation cokernels in Iwasawa theory. (English) Zbl 1094.11039 Am. J. Math. 127, No. 4, 851-877 (2005). Reviewer: Jean-François Jaulent (Talence) MSC: 11R23 PDF BibTeX XML Cite \textit{M. Le Floc'h} et al., Am. J. Math. 127, No. 4, 851--877 (2005; Zbl 1094.11039) Full Text: DOI OpenURL
Azizi, Abdelmalek Group theory and the capitulation problem for certain biquadratic fields. (English) Zbl 1075.11072 Kalla, Shyam L. (ed.) et al., Proceedings of the international conference on mathematics and its applications, ICMA 2004, Kuwait, April 5–7, 2004. Kuwait: Kuwait University, Department of Mathematics and Computer Science; Kuwait: Kuwait Foundation for the Advancement of Sciences (KFAS). 43-51 (2005). Reviewer: Elliot Benjamin (Swanville) MSC: 11R37 PDF BibTeX XML Cite \textit{A. Azizi}, in: Proceedings of the international conference on mathematics and its applications, ICMA 2004, Kuwait, April 5--7, 2004. Kuwait: Kuwait University, Department of Mathematics and Computer Science; Kuwait: Kuwait Foundation for the Advancement of Sciences (KFAS). 43--51 (2005; Zbl 1075.11072) OpenURL
Ayadi, Mohammed The Hilbert tower of cyclic cubic fields whose 3-class number is 9. (La tour de Hilbert des corps cubiques cycliques dont le 3-nombre de classes est 9.) (French) Zbl 1102.11061 Ann. Sci. Math. Qué. 28, No. 1-2, 29-35 (2004). Reviewer: Charles Parry (Blacksburg) MSC: 11R37 11R16 11R29 PDF BibTeX XML Cite \textit{M. Ayadi}, Ann. Sci. Math. Qué. 28, No. 1--2, 29--35 (2004; Zbl 1102.11061) OpenURL
Ozaki, Manabu Construction of \(\mathbb Z_p\)-extensions with prescribed Iwasawa modules. (English) Zbl 1142.11368 J. Math. Soc. Japan 56, No. 3, 787-801 (2004). MSC: 11R23 11R29 PDF BibTeX XML Cite \textit{M. Ozaki}, J. Math. Soc. Japan 56, No. 3, 787--801 (2004; Zbl 1142.11368) Full Text: DOI OpenURL
Gruenberg, K. W.; Weiss, A. Capitulation and transfer triples. (English) Zbl 1055.11069 Proc. Lond. Math. Soc., III. Ser. 87, No. 2, 273-290 (2003). Reviewer: Ken Yamamura (Yokosuka) MSC: 11R33 20J99 PDF BibTeX XML Cite \textit{K. W. Gruenberg} and \textit{A. Weiss}, Proc. Lond. Math. Soc. (3) 87, No. 2, 273--290 (2003; Zbl 1055.11069) Full Text: DOI OpenURL
Fleckinger, Vincent; Thiébaud, Caroline Idéaux ambiges dans les corps de fonctions. (Ambiguous ideals in function fields). (French) Zbl 1027.11084 J. Number Theory 100, No. 2, 217-228 (2003). Reviewer: Andreas Schweizer (Seoul) MSC: 11R37 11R58 11R60 PDF BibTeX XML Cite \textit{V. Fleckinger} and \textit{C. Thiébaud}, J. Number Theory 100, No. 2, 217--228 (2003; Zbl 1027.11084) Full Text: DOI OpenURL
Azizi, Abdelmalek; Mouhib, Ali Capitulation of 2-ideal classes of \({\mathbb Q}(\sqrt{2},\sqrt{d})\) where \(d\) is a square-free natural integer. (Capitulation des 2-classes d’idéaux de \({\mathbb Q}(\sqrt{2},\sqrt{d})\) où \(d\) est un entier naturel sans facteurs carrés.) (French) Zbl 1077.11078 Acta Arith. 109, No. 1, 27-63 (2003). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R27 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{A. Mouhib}, Acta Arith. 109, No. 1, 27--63 (2003; Zbl 1077.11078) Full Text: DOI OpenURL
Gras, Georges Class field theory. From theory to practice. (English) Zbl 1019.11032 Springer Monographs in Mathematics. Berlin: Springer. xiii, 491 p. EUR 79.95/net; sFr 133.00; £56.00; $ 79.95 (2003). Reviewer: Wladyslaw Narkiewicz (Wrocław) MSC: 11R37 11-01 11-02 11R29 11R20 11S31 PDF BibTeX XML Cite \textit{G. Gras}, Class field theory. From theory to practice. Berlin: Springer (2003; Zbl 1019.11032) OpenURL
Riese, Udo Integral representations for the alternating groups. (English) Zbl 1005.20010 Proc. Am. Math. Soc. 130, No. 12, 3515-3518 (2002). Reviewer: Jürgen Ritter (Augsburg) MSC: 20C10 20C30 PDF BibTeX XML Cite \textit{U. Riese}, Proc. Am. Math. Soc. 130, No. 12, 3515--3518 (2002; Zbl 1005.20010) Full Text: DOI OpenURL
Azizi, Abdelmalek Sur une question de capitulation. (On the capitulation problem). (French) Zbl 1010.11061 Proc. Am. Math. Soc. 130, No. 8, 2197-2202 (2002). Reviewer: Florence Soriano-Gafiuk (Schweyen) MSC: 11R27 11R16 11R37 PDF BibTeX XML Cite \textit{A. Azizi}, Proc. Am. Math. Soc. 130, No. 8, 2197--2202 (2002; Zbl 1010.11061) Full Text: DOI OpenURL
Suzuki, Hiroshi On the capitulation problem. (English) Zbl 1032.11048 Miyake, Katsuya (ed.), Class field theory - its centenary and prospect. Proceedings of the 7th MSJ International Research Institute of the Mathematical Society of Japan, Tokyo, Japan, June 3-12, 1998. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 30, 483-507 (2001). Reviewer: T.Takeuchi (Niigata) MSC: 11R37 PDF BibTeX XML Cite \textit{H. Suzuki}, Adv. Stud. Pure Math. 30, 483--507 (2001; Zbl 1032.11048) OpenURL
Ayadi, Mohammed; Azizi, Abdelmalek; Ismaili, Moulay Chrif The capitulation problem for certain number fields. (English) Zbl 1015.11055 Miyake, Katsuya (ed.), Class field theory - its centenary and prospect. Proceedings of the 7th MSJ International Research Institute of the Mathematical Society of Japan, Tokyo, Japan, June 3-12, 1998. Tokyo: Mathematical Society of Japan. Adv. Stud. Pure Math. 30, 467-482 (2001). Reviewer: T.Takeuchi (Niigata) MSC: 11R29 11R37 PDF BibTeX XML Cite \textit{M. Ayadi} et al., Adv. Stud. Pure Math. 30, 467--482 (2001; Zbl 1015.11055) OpenURL
Fukuda, Takashi; Komatsu, Keiichi On Iwasawa \(\lambda_3\)-invariants of cyclic cubic fields of prime conductor. (English) Zbl 0993.11056 Math. Comput. 70, No. 236, 1707-1712 (2001). Reviewer: Franz Lemmermeyer (San Marcos) MSC: 11R23 11R27 11Y40 11R18 PDF BibTeX XML Cite \textit{T. Fukuda} and \textit{K. Komatsu}, Math. Comput. 70, No. 236, 1707--1712 (2001; Zbl 0993.11056) Full Text: DOI OpenURL
Sumida, Hiroki On capitulation of \(S\)-ideals in \(\mathbb{Z}_p\). (English) Zbl 0997.11090 J. Number Theory 86, No. 1, 163-174 (2001). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R23 11R29 PDF BibTeX XML Cite \textit{H. Sumida}, J. Number Theory 86, No. 1, 163--174 (2001; Zbl 0997.11090) Full Text: DOI OpenURL
Gruenberg, K. W.; Weiss, A. Capitulation and transfer kernels. (English) Zbl 1009.11061 J. Théor. Nombres Bordx. 12, No. 1, 219-226 (2000). Reviewer: Florence Soriano-Gafiuk (Schweyen) MSC: 11R37 11R20 11R33 PDF BibTeX XML Cite \textit{K. W. Gruenberg} and \textit{A. Weiss}, J. Théor. Nombres Bordx. 12, No. 1, 219--226 (2000; Zbl 1009.11061) Full Text: DOI Numdam EuDML OpenURL
Khare, Chandrashekhar; Prasad, Dipendra On the Steinitz module and capitulation of ideals. (English) Zbl 0971.11055 Nagoya Math. J. 160, 1-15 (2000). Reviewer: Władysław Narkiewicz (Wrocław) MSC: 11R29 11R37 14H30 PDF BibTeX XML Cite \textit{C. Khare} and \textit{D. Prasad}, Nagoya Math. J. 160, 1--15 (2000; Zbl 0971.11055) Full Text: DOI OpenURL
Azizi, Abdelmalek Capitulation of the 2-ideal classes of \(\mathbb{Q}(\sqrt{p_1p_2},i)\) where \(p_1\) and \(p_2\) are primes such that \(p_1\equiv 1 \pmod 8\), \(p_2\equiv 5 \pmod 8\) and \(\left(\frac{p_1}{p_2}\right)=-1\). (English) Zbl 1003.11050 Boulagouaz, M’hammed (ed.) et al., Algebra and number theory. Proceedings of a conference, Fez, Morocco. New York, NY: Marcel Dekker. Lect. Notes Pure Appl. Math. 208, 13-19 (2000). Reviewer: Charles Parry (Blacksburg) MSC: 11R29 11R16 11R11 PDF BibTeX XML Cite \textit{A. Azizi}, Lect. Notes Pure Appl. Math. 208, 13--19 (2000; Zbl 1003.11050) OpenURL
Azizi, Abdelmalek On the capitulation of the 2-class group of \(\mathbb{K}=\mathbb{Q}(\sqrt{2pq}, i)\) where \(p\equiv -q\equiv 1\mod 4\). (Sur la capitulation des 2-classes d’idéaux de \(\mathbb{K}=\mathbb{Q}(\sqrt{2pq},i)\) où \(p\equiv-q\equiv 1\mod 4\).) (French) Zbl 0953.11033 Acta Arith. 94, No. 4, 383-399 (2000). Reviewer: Florence Soriano-Gafiuk (Schweyen) MSC: 11R27 11R16 PDF BibTeX XML Cite \textit{A. Azizi}, Acta Arith. 94, No. 4, 383--399 (2000; Zbl 0953.11033) Full Text: DOI EuDML OpenURL
Kolster, Manfred; Movahhedi, Abbas Galois co-descent for étale wild kernels and capitulation. (English) Zbl 0951.11029 Ann. Inst. Fourier 50, No. 1, 35-65 (2000). Reviewer: T.Nguyen Quang Do (Besançon) MSC: 11R23 11R34 11R70 PDF BibTeX XML Cite \textit{M. Kolster} and \textit{A. Movahhedi}, Ann. Inst. Fourier 50, No. 1, 35--65 (2000; Zbl 0951.11029) Full Text: DOI Numdam EuDML OpenURL
Lemmermeyer, Franz Ideal class groups of cyclotomic number fields. II. (English) Zbl 0901.11031 Acta Arith. 84, No. 1, 59-70 (1998). Reviewer: T.Metsänkylä (Turku) MSC: 11R18 11R29 11R21 11R37 PDF BibTeX XML Cite \textit{F. Lemmermeyer}, Acta Arith. 84, No. 1, 59--70 (1998; Zbl 0901.11031) Full Text: DOI arXiv EuDML OpenURL
Gras, Georges Making ideals principal by absolute abelian extensions. (Principalisation d’idéaux par extensions absolument abéliennes.) (French) Zbl 0869.11088 J. Number Theory 62, No. 2, 403-421 (1997). Reviewer: F.Lemmermeyer (Heidelberg) MSC: 11R29 11R20 PDF BibTeX XML Cite \textit{G. Gras}, J. Number Theory 62, No. 2, 403--421 (1997; Zbl 0869.11088) Full Text: DOI arXiv OpenURL
Maire, C. \(T\)-\(S\) capitulation. (French) Zbl 1254.11100 Publ. Math. Fac. Sci. Besançon, Théor. Nombres, 1994/95–1995/96, 33 pp. (1997). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11R37 11R29 PDF BibTeX XML Cite \textit{C. Maire}, Publ. Math. Fac. Sci. Besançon, Théor. Nombres, 33 pp. (1997; Zbl 1254.11100) OpenURL
Fukuda, Takashi On the vanishing of Iwasawa invariants of certain cyclic extensions of \(\mathbb{Q}\) with prime degree. (English) Zbl 0899.11052 Proc. Japan Acad., Ser. A 73, No. 6, 108-110 (1997). Reviewer: Gabriel D.Villa-Salvador (México) MSC: 11R23 11R18 PDF BibTeX XML Cite \textit{T. Fukuda}, Proc. Japan Acad., Ser. A 73, No. 6, 108--110 (1997; Zbl 0899.11052) Full Text: DOI OpenURL
Ozaki, Manabu The class group of \(\mathbb{Z}_p\)-extensions over totally real number fields. (English) Zbl 0896.11044 Tôhoku Math. J., II. Ser. 49, No. 3, 431-435 (1997). Reviewer: F.Lemmermeyer (Heidelberg) MSC: 11R23 11R29 PDF BibTeX XML Cite \textit{M. Ozaki}, Tôhoku Math. J. (2) 49, No. 3, 431--435 (1997; Zbl 0896.11044) Full Text: DOI OpenURL
Azizi, Abdelmalek Capitulation of the \(2\)-class group of \(\mathbb Q(\sqrt d,i)\). (Sur la capitulation des \(2\)-classes d’idéaux de \(\mathbb Q(\sqrt d,i)\).) (French) Zbl 0885.11061 C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 2, 127-130 (1997). Reviewer: Florence Soriano (Metz) MSC: 11R37 11R16 11R29 11R32 PDF BibTeX XML Cite \textit{A. Azizi}, C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 2, 127--130 (1997; Zbl 0885.11061) Full Text: DOI OpenURL
Fukuda, Takashi; Komatsu, Keiichi A capitulation problem and Greenberg’s conjecture on real quadratic fields. (English) Zbl 0860.11067 Math. Comput. 65, No. 213, 313-318 (1996). Reviewer: T.Takeuchi (Niigata) MSC: 11R23 11Y40 11R11 PDF BibTeX XML Cite \textit{T. Fukuda} and \textit{K. Komatsu}, Math. Comput. 65, No. 213, 313--318 (1996; Zbl 0860.11067) Full Text: DOI OpenURL
Ozaki, Manabu A note on the capitulation in \(\mathbb{Z}_ p\)-extensions. (English) Zbl 0857.11064 Proc. Japan Acad., Ser. A 71, No. 9, 218-219 (1995). Reviewer: I.Fesenko (Nottingham) MSC: 11S31 11R23 PDF BibTeX XML Cite \textit{M. Ozaki}, Proc. Japan Acad., Ser. A 71, No. 9, 218--219 (1995; Zbl 0857.11064) Full Text: DOI OpenURL