Bouvier, Lyliane; Payan, Jean-Jacques Sur la structure galoisienne du groupe des unités d’un corps abélien de type \((p,p)\). (French) Zbl 0387.12007 Ann. Inst. Fourier 29, No. 1, 171-187 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 2 ReviewsCited in 3 Documents MSC: 11R32 Galois theory 11R18 Cyclotomic extensions 11R27 Units and factorization Keywords:ABELIAN EXTENSION; GROUP OF UNITS; GALOIS THEORY PDF BibTeX XML Cite \textit{L. Bouvier} and \textit{J.-J. Payan}, Ann. Inst. Fourier 29, No. 1, 171--187 (1979; Zbl 0387.12007) Full Text: DOI Numdam EuDML References: [1] A. BRUMER, On the group of units of an absolutely cyclic number field of prime degree, J. Math. Soc. Japan, (1969), 357-358. · Zbl 0188.35301 [2] H. CARTAN et S. EILENBERG, Homological algebra, Princeton Univ. Press, Princeton, N.J., 1956. · Zbl 0075.24305 [3] C.W. CURTIS et I. REINER, Representation theory of finite groups and associative algebras, Pure and Appl. Math., vol XI, Interscience, New York, 1962. · Zbl 0131.25601 [4] G. GRAS, 1ère partie: sur LES ℓ-classes d’idéaux dans LES extensions cycliques relatives de degré premier ℓ, Annales de l’Institut Fourier, 23, 3 (1973), 1-48. · Zbl 0276.12013 [5] KISILEVSKI, Some results related to Hilbert’s theorem 94, J. Number theory, 2 (1970), 199-206. · Zbl 0216.04701 [6] T. KUBOTA, Uber den bizyklischen biquadratischen zahlkörper, Nagoya Math. J., 10 (1956), 65-85. · Zbl 0074.03001 [7] S. KURODA, Uber die klassenzahlen algebraischer zahlkörper, Nagoya Math. J., 1 (1950), 1-10. · Zbl 0037.16101 [8] N. MOSER, Unités et nombre de classes d’une extension galoisienne de Q, Thèse de 3e cycle, Grenoble (1975). · Zbl 0313.12002 [9] J. MARTINET, A propos de classes d’idéaux, Séminaire de Th. des Nombres, Bordeaux (1971-1972), exposé n° 5. · Zbl 0285.12006 [10] H. NEHRKORN, Über absolute idealklassengruppen und einheiten in algebraischen zahlkörpern, Abh. Math. Sem. Univ. Hamburg, 9 (1933), 319-334. · JFM 59.0165.02 [11] I. REINER, A survey of integral representation theory, Bull. of Ann. Math. Soc., vol. 16, n° 2 (1970). · Zbl 0194.04701 [12] J.P. SERRE, Corps locaux, Hermann, Paris, 1968. [13] C.D. WALTER, Brauer’s class number relation, Acta Arithmetica, (à paraître). · Zbl 0339.12007 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.