TY - JOUR
T1 - On the cyclotomic unit group and the ideal class group of a real abelian number field
AU - Ozaki, Manabu
N1 - Copyright:
Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.
PY - 1997/6
Y1 - 1997/6
N2 - LetKbe a real abelian number field satisfying certain conditions andKnthenth layer of the cyclotomic Zp-extension ofK. We study the relations between thep-Sylow subgroup of the ideal class group and that of the unit group modulo the cyclotomic unit group ofKn. Supposing that Greenberg's conjecture is valid, we shall show that these two groups are isomorphic as Galois modules for sufficiently largen.
AB - LetKbe a real abelian number field satisfying certain conditions andKnthenth layer of the cyclotomic Zp-extension ofK. We study the relations between thep-Sylow subgroup of the ideal class group and that of the unit group modulo the cyclotomic unit group ofKn. Supposing that Greenberg's conjecture is valid, we shall show that these two groups are isomorphic as Galois modules for sufficiently largen.
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U2 - 10.1006/jnth.1997.2086
DO - 10.1006/jnth.1997.2086
M3 - Article
AN - SCOPUS:0031161760
VL - 64
SP - 211
EP - 222
JO - Journal of Number Theory
JF - Journal of Number Theory
SN - 0022-314X
IS - 2
ER -