Chems-Eddin, Mohamed Mahmoud; Zekhnini, Abdelkader; Azizi, Abdelmalek Unit groups of some multiquadratic number fields of degree 16. (English) Zbl 1514.11070 São Paulo J. Math. Sci. 16, No. 2, 1091-1096 (2022). Reviewer: Artūras Dubickas (Vilnius) MSC: 11R04 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{M. M. Chems-Eddin} et al., São Paulo J. Math. Sci. 16, No. 2, 1091--1096 (2022; Zbl 1514.11070) Full Text: DOI
Benjamin, Elliot; Snyder, C. Determination of all imaginary quadratic fields for which their Hilbert 2-class fields have 2-class groups of rank 2. (English) Zbl 07569765 J. Number Theory 238, 1012-1043 (2022). Reviewer: Francesco Battistoni (Milano) MSC: 11R29 20D15 PDF BibTeX XML Cite \textit{E. Benjamin} and \textit{C. Snyder}, J. Number Theory 238, 1012--1043 (2022; Zbl 07569765) Full Text: DOI
Chems-Eddin, Mohamed Mahmoud Unit groups of some multiquadratic number fields and 2-class groups. (English) Zbl 1513.11178 Period. Math. Hung. 84, No. 2, 235-249 (2022). Reviewer: Nikolai L. Manev (Sofia) MSC: 11R04 11R27 11R29 11R37 PDF BibTeX XML Cite \textit{M. M. Chems-Eddin}, Period. Math. Hung. 84, No. 2, 235--249 (2022; Zbl 1513.11178) Full Text: DOI arXiv
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
Chems-Eddin, Mohamed Mahmoud; Zekhnini, Abdelkader; Azizi, Abdelmalek Units and 2-class field towers of some multiquadratic number fields. (English) Zbl 1455.11140 Turk. J. Math. 44, No. 4, 1466-1483 (2020). Reviewer: Toufik Zaïmi (Riyadh) MSC: 11R04 11R11 11R27 11R29 11R39 PDF BibTeX XML Cite \textit{M. M. Chems-Eddin} et al., Turk. J. Math. 44, No. 4, 1466--1483 (2020; Zbl 1455.11140) Full Text: DOI arXiv
Azizi, Abdelmalek; Rezzougui, Mohammed; Taous, Mohammed; Zekhnini, Abdelkader On the Hilbert 2-class field of some quadratic number fields. (English) Zbl 1457.11151 Int. J. Number Theory 15, No. 4, 807-824 (2019). Reviewer: Elliot Benjamin (Winterport) MSC: 11R29 11R11 11R32 11R37 20D15 PDF BibTeX XML Cite \textit{A. Azizi} et al., Int. J. Number Theory 15, No. 4, 807--824 (2019; Zbl 1457.11151) Full Text: DOI
Benjamin, Elliot; Snyder, C. On the rank of the 2-class group of the Hilbert 2-class field of some quadratic fields. (English) Zbl 1445.11127 Q. J. Math. 69, No. 4, 1163-1193 (2018). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R29 11R11 PDF BibTeX XML Cite \textit{E. Benjamin} and \textit{C. Snyder}, Q. J. Math. 69, No. 4, 1163--1193 (2018; Zbl 1445.11127) Full Text: DOI
Azizi, Abdelmalek; Jerrari, Idriss; Talbi, Mohammed Unramified extensions of some cyclic quartic fields. (English) Zbl 1424.11154 Bol. Soc. Parana. Mat. (3) 36, No. 1, 215-221 (2018). MSC: 11R16 11R27 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Bol. Soc. Parana. Mat. (3) 36, No. 1, 215--221 (2018; Zbl 1424.11154) Full Text: Link
Benjamin, Elliot Corrigendum to: “Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group”. (English) Zbl 1377.11115 J. Number Theory 180, 787-789 (2017). MSC: 11R29 11R11 PDF BibTeX XML Cite \textit{E. Benjamin}, J. Number Theory 180, 787--789 (2017; Zbl 1377.11115) Full Text: DOI
Benjamin, Elliot; Snyder, C. Some real quadratic number fields whose Hilbert 2-class fields have class number congruent to 2 modulo 4. (English) Zbl 1401.11143 Acta Arith. 177, No. 4, 375-392 (2017). Reviewer: Alessandro Cobbe (Neubiberg) MSC: 11R29 20D15 PDF BibTeX XML Cite \textit{E. Benjamin} and \textit{C. Snyder}, Acta Arith. 177, No. 4, 375--392 (2017; Zbl 1401.11143) Full Text: DOI
Benjamin, Elliot Some real quadratic number fields with their Hilbert 2-class field having cyclic 2-class group. (English) Zbl 1377.11114 J. Number Theory 173, 529-546 (2017); corrigendum ibid. 180, 787-789 (2017). Reviewer: Alessandro Cobbe (Neubiberg) MSC: 11R29 11R11 PDF BibTeX XML Cite \textit{E. Benjamin}, J. Number Theory 173, 529--546 (2017; Zbl 1377.11114) Full Text: DOI
Azizi, Abdelmalek; Talbi, Mohammed; Talbi, Mohamed On the Hilbert tower of certain fields. (Sur la tour de Hilbert de certains corps.) (French. English summary) Zbl 1415.11168 Bol. Soc. Parana. Mat. (3) 34, No. 2, 107-112 (2016). MSC: 11R37 11R16 11R27 11R29 PDF BibTeX XML Cite \textit{A. Azizi} et al., Bol. Soc. Parana. Mat. (3) 34, No. 2, 107--112 (2016; Zbl 1415.11168) Full Text: Link
Azizi, Abdelmalek; Zekhnini, Abdelkader; Taous, Mohammed Coclass of \(\mathrm{Gal}(\Bbbk_2^{(2)}/\Bbbk)\) for some fields \(\Bbbk=\mathbb{Q}(\sqrt{p_1p_2q},\sqrt{-1})\) with 2-class groups of types (2,2,2). (English) Zbl 1335.11091 J. Algebra Appl. 15, No. 2, Article ID 1650027, 26 p. (2016). Reviewer: John D. Dixon (Ottawa) MSC: 11R16 11R11 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., J. Algebra Appl. 15, No. 2, Article ID 1650027, 26 p. (2016; Zbl 1335.11091) Full Text: DOI
Wang, Victor Y. On Hilbert 2-class fields and 2-towers of imaginary quadratic number fields. (English) Zbl 1334.11085 J. Number Theory 160, 492-515 (2016). Reviewer: Alessandro Cobbe (Neubiberg) MSC: 11R37 11R29 11R32 11R11 PDF BibTeX XML Cite \textit{V. Y. Wang}, J. Number Theory 160, 492--515 (2016; Zbl 1334.11085) Full Text: DOI arXiv
Azizi, Abdelmalek; Taous, Mohammed; Zekhnini, Abdelkader On the rank of the 2-class group of \(\mathbb Q(\sqrt{p},\sqrt{q},\sqrt{-1})\). (English) Zbl 1340.11086 Period. Math. Hung. 69, No. 2, 231-238 (2014). Reviewer: Nikolai L. Manev (Sofia) MSC: 11R11 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Azizi} et al., Period. Math. Hung. 69, No. 2, 231--238 (2014; Zbl 1340.11086) Full Text: DOI arXiv
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
Mouhib, A. On \(2\)-class field towers of some real quadratic number fields with \(2\)-class groups of rank \(3\). (English) Zbl 1302.11090 Ill. J. Math. 57, No. 4, 1009-1018 (2013). MSC: 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Mouhib}, Ill. J. Math. 57, No. 4, 1009--1018 (2013; Zbl 1302.11090) Full Text: Euclid
Jung, Hwanyup Hilbert 2-class field towers of imaginary quadratic function fields. (English) Zbl 1368.11119 Bull. Korean Math. Soc. 50, No. 3, 1049-1060 (2013). Reviewer: Gabriel D. Villa-Salvador (México D. F.) MSC: 11R58 11R11 PDF BibTeX XML Cite \textit{H. Jung}, Bull. Korean Math. Soc. 50, No. 3, 1049--1060 (2013; Zbl 1368.11119) Full Text: DOI Link
Mouhib, A. Infinite Hilbert 2-class field tower of quadratic number fields. (English) Zbl 1211.11127 Acta Arith. 145, No. 3, 267-272 (2010); acknowledgement of priority ibid. 167, No. 3, 299 (2015). Reviewer: Elliot Benjamin (Swanville) MSC: 11R29 11R32 11R37 PDF BibTeX XML Cite \textit{A. Mouhib}, Acta Arith. 145, No. 3, 267--272 (2010; Zbl 1211.11127) Full Text: DOI
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
Gerth, Frank III Densities for some real quadratic fields with infinite Hilbert 2-class field towers. (English) Zbl 1090.11067 J. Number Theory 118, No. 1, 90-97 (2006). Reviewer: Franz Lemmermeyer (Bilkent) MSC: 11R11 11R29 11R37 PDF BibTeX XML Cite \textit{F. Gerth III}, J. Number Theory 118, No. 1, 90--97 (2006; Zbl 1090.11067) Full Text: DOI
Azizi, Abdelmalek; Mouhib, Ali Existence of biquadratic fields \(K\) for which the Galois group of the second Hilbert 2-class field with respect to \(K\) is semidihedral. (Sur l’existence des corps biquadratiques \(K\) dont le groupe de Galois du deuxième \(2\)-corps de classes de Hilbert par rapport à \(K\) est semi-diédral.) (French) Zbl 1122.11074 Arch. Math., Brno 41, No. 3, 253-263 (2005). Reviewer: Radan Kučera (Brno) MSC: 11R27 11R37 PDF BibTeX XML Cite \textit{A. Azizi} and \textit{A. Mouhib}, Arch. Math., Brno 41, No. 3, 253--263 (2005; Zbl 1122.11074) Full Text: EuDML EMIS
Gerth, Frank III Some real quadratic fields with infinite Hilbert 2-class field towers. (English) Zbl 1075.11066 Jap. J. Math., New Ser. 31, No. 1, 175-181 (2005). Reviewer: Elliot Benjamin (Swanville) MSC: 11R11 11R29 PDF BibTeX XML Cite \textit{F. Gerth III}, Jpn. J. Math., New Ser. 31, No. 1, 175--181 (2005; Zbl 1075.11066)
Gerth, Frank III A density result for some imaginary quadratic fields with infinite Hilbert 2-class field towers. (English) Zbl 1054.11055 Arch. Math. 82, No. 1, 23-27 (2004). Reviewer: Elliot Benjamin (Swanville) MSC: 11R29 11R37 11R45 PDF BibTeX XML Cite \textit{F. Gerth III}, Arch. Math. 82, No. 1, 23--27 (2004; Zbl 1054.11055) Full Text: DOI
Benjamin, E.; Lemmermeyer, F.; Snyder, C. Imaginary quadratic fields with \(Cl_2(k)\simeq (2,2,2)\). (English) Zbl 1045.11077 J. Number Theory 103, No. 1, 38-70 (2003). Reviewer: Charles Parry (Blacksburg) MSC: 11R29 11R11 PDF BibTeX XML Cite \textit{E. Benjamin} et al., J. Number Theory 103, No. 1, 38--70 (2003; Zbl 1045.11077) Full Text: DOI
Gerth, Frank III Quadratic fields with infinite Hilbert 2-class field towers. (English) Zbl 1064.11073 Acta Arith. 106, No. 2, 151-158 (2003). Reviewer: Charles Parry (Blacksburg) MSC: 11R37 11R29 11R45 PDF BibTeX XML Cite \textit{F. Gerth III}, Acta Arith. 106, No. 2, 151--158 (2003; Zbl 1064.11073) Full Text: DOI
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)
Benjamin, E.; Lemmermeyer, F.; Snyder, C. Imaginary quadratic fields \(k\) with \(\text{Cl}_ 2(k)\simeq(2,2^ m)\) and rank \(\text{Cl}_ 2(k^ 1)=2\). (English) Zbl 1063.11038 Pac. J. Math. 198, No. 1, 15-31 (2001). Reviewer: Charles Parry (Blacksburg) MSC: 11R29 11R11 PDF BibTeX XML Cite \textit{E. Benjamin} et al., Pac. J. Math. 198, No. 1, 15--31 (2001; Zbl 1063.11038) Full Text: DOI
Benjamin, Elliot Lower bounds on the 2-class number of the Hilbert 2-class field of quadratic number fields with 2-class number greater than or equal to 16. (English) Zbl 0936.11064 Far East J. Math. Sci. (FJMS) 1, No. 1, 101-119 (1999). Reviewer: Franz Lemmermeyer (Bonn) MSC: 11R29 11R11 11R37 PDF BibTeX XML Cite \textit{E. Benjamin}, Far East J. Math. Sci. (FJMS) 1, No. 1, 101--119 (1999; Zbl 0936.11064)
Maire, Christian A refinement of the Golod-Shafarevich theorem. (Un raffinement du théorème de Golod-Šafarevič.) (French) Zbl 0923.11158 Nagoya Math. J. 150, 1-11 (1998). Reviewer: H.Koch (Berlin) MSC: 11R37 PDF BibTeX XML Cite \textit{C. Maire}, Nagoya Math. J. 150, 1--11 (1998; Zbl 0923.11158) Full Text: DOI
Schneiders, Ursula Estimating the 2-rank of cubic fields by Selmer groups of elliptic curves. (English) Zbl 0870.11033 J. Number Theory 62, No. 2, 375-396 (1997). Reviewer: F.Lemmermeyer (Heidelberg) MSC: 11G05 11R16 11R29 11R37 PDF BibTeX XML Cite \textit{U. Schneiders}, J. Number Theory 62, No. 2, 375--396 (1997; Zbl 0870.11033) Full Text: DOI
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
Benjamin, Elliot Lower bounds on the 2-class number of the 2-Hilbert class field of imaginary quadratic number fields with elementary 2-class group of rank 3. (English) Zbl 0863.11075 Houston J. Math. 22, No. 1, 11-37 (1996). Reviewer: C.Parry (Blacksburg) MSC: 11R29 11R11 11R37 PDF BibTeX XML Cite \textit{E. Benjamin}, Houston J. Math. 22, No. 1, 11--37 (1996; Zbl 0863.11075)
Benjamin, Elliot; Snyder, C. Real quadratic number fields with 2-class group of type \((2,2)\). (English) Zbl 0847.11058 Math. Scand. 76, No. 2, 161-178 (1995). Reviewer: H.Yokoi (Iwasaki) MSC: 11R29 11R11 PDF BibTeX XML Cite \textit{E. Benjamin} and \textit{C. Snyder}, Math. Scand. 76, No. 2, 161--178 (1995; Zbl 0847.11058) Full Text: DOI EuDML
Lemmermeyer, Franz On 2-class field towers of imaginary quadratic number fields. (English) Zbl 0826.11052 J. Théor. Nombres Bordx. 6, No. 2, 261-272 (1994). Reviewer: H.Koch (Berlin) MSC: 11R37 11R11 PDF BibTeX XML Cite \textit{F. Lemmermeyer}, J. Théor. Nombres Bordx. 6, No. 2, 261--272 (1994; Zbl 0826.11052) Full Text: DOI arXiv Numdam EuDML EMIS
Benjamin, Elliot Remarks concerning the 2-Hilbert class field of imaginary quadratic number fields. (English) Zbl 0806.11047 Bull. Aust. Math. Soc. 48, No. 3, 379-383 (1993). Reviewer: C.Parry (Blacksburg) MSC: 11R29 11R37 11R11 PDF BibTeX XML Cite \textit{E. Benjamin}, Bull. Aust. Math. Soc. 48, No. 3, 379--383 (1993; Zbl 0806.11047) Full Text: DOI
Fujisaki, Genjiro A note on a paper of Iwasawa. (English) Zbl 0705.11069 Proc. Japan Acad., Ser. A 66, No. 2, 61-64 (1990). Reviewer: H.Yokoi MSC: 11R37 11R20 11R29 PDF BibTeX XML Cite \textit{G. Fujisaki}, Proc. Japan Acad., Ser. A 66, No. 2, 61--64 (1990; Zbl 0705.11069) Full Text: DOI