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- Title
Galois module structure of the p--subgroup of the minus part of the ray class group in ℤ<sub>p</sub>--extensions.
- Authors
Jarquín-Zárate, F.; Villa-Salvador, G.
- Abstract
Let p be an odd prime number and let L/K be an arbitrary finite Galois ℤp-extension of p-cyclotomic fields of CM-type. In this paper, assuming that the Iwasawa µ- invariants of K and L are zero, we obtain the Galois module structure of 퇒항- (p), the p-subgroup of the minus part of the ray class group of L, and of p퇒항- the elements of 퇒항- (p) of order a divisor of p, associated to the modulus 프 B of L induced by a modulus 프. of K, which contains in its support the non-p-prime divisors of K+ ramified in L+ and split in K, and also contains in its support a finite collection of non-p-prime divisors of K+ that do not ramify in L+; they may split in K or be inert in K. That is, we obtain explicitly the decomposition of 퇒항- (p) (of p퇒항-) as a direct sum of indecomposable ℤp[G]-modules (픽p[G]-modules) with respect to the modulus 항.
- Subjects
PRIME numbers; GALOIS modules (Algebra); CYCLOTOMIC fields; INVARIANTS (Mathematics); MATHEMATICAL decomposition
- Publication
Palestine Journal of Mathematics, 2014, Vol 3, Issue 1, p1
- ISSN
2219-5688
- Publication type
Article