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On the Galois module structure of ideal class groups
- Source :
- Nagoya Math. J. 164 (2001), 133-146
- Publication Year :
- 2001
- Publisher :
- Cambridge University Press (CUP), 2001.
-
Abstract
- Let K/k be a Galois extension of a number field of degree n and p a prime number which does not divide n. The study of the p-rank of the ideal class group of K by using those of intermediate fields of K/k has been made by Iwasawa, Masley et al., attaining the results obtained under respective constraining assumptions. In the present paper we shall show that we can remove these assumptions, and give more general results under a unified viewpoint. Finally, we shall add a remark on the class numbers of cyclic extensions of prime degree of Q.
- Subjects :
- Discrete mathematics
Non-abelian class field theory
010308 nuclear & particles physics
Galois cohomology
Mathematics::Number Theory
General Mathematics
Fundamental theorem of Galois theory
010102 general mathematics
Galois group
Abelian extension
11R29
Splitting of prime ideals in Galois extensions
Galois module
01 natural sciences
Embedding problem
symbols.namesake
0103 physical sciences
symbols
0101 mathematics
Mathematics
Subjects
Details
- ISSN :
- 21526842 and 00277630
- Volume :
- 164
- Database :
- OpenAIRE
- Journal :
- Nagoya Mathematical Journal
- Accession number :
- edsair.doi.dedup.....2b16c7b8dc0df4f04cfc2287f28f5112