Group-theoretic constraints on the structure of the class group

Cornell, Gary; Rosen, Michael

doi:10.1016/0022-314x(81)90026-3

Cited by 19 publications

(9 citation statements)

References 4 publications

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“…It is well known that K 2 Z ∼ = Z/2. Note that j · tr = g∈G g. The lemma follows from [CR,Proposition 5]. Proof.…”

Section: The 3-primary Part Of the Tame Kernel Ofmentioning

confidence: 99%

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Tame kernels of cubic cyclic fields

Zhou

2006

Acta Arith.

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“…It is well known that K 2 Z ∼ = Z/2. Note that j · tr = g∈G g. The lemma follows from [CR,Proposition 5]. Proof.…”

Section: The 3-primary Part Of the Tame Kernel Ofmentioning

confidence: 99%

“…Suppose T = Gal(F/Q) and 3-rank A T F = s. By the well-known fact that 3-rank A T F is one less than the number of ramified primes, we have s = r − 1. From the proof of [CR,Proposition 5], we have the following cases:…”

Section: The 3-primary Part Of the Tame Kernel Ofmentioning

confidence: 99%

Tame kernels of cubic cyclic fields

Zhou

2006

Acta Arith.

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“…We next state two propositions which extend slightly the results of Iwasawa [5], Cornell-Rosen [3] or Cornell [2]. Though the heart of the proof may be found in their original arguments, we present here an approach via the direct use of the kernels of norm maps, which seems to us more easily comprehensible.…”

Section: Proof One May Easily Check Thatmentioning

confidence: 66%

On the Galois module structure of ideal class groups

Komatsu¹,

Nakano²

2001

Nagoya Mathematical Journal

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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 .

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“…Although we omit the details, the results of [13,17,18], together with those of [1,2,8,11,12,15,16], enable us to determine the structure of C(k") or C~(k") for several imaginary abelian fields k" outside 2? (cf.…”

Section: C~(f) Sk the Sylow P-subgroup Of C~ (K) I The Natural Map mentioning

confidence: 99%

On the Ideal Class Groups of Imaginary Abelian Fields with Small Conductor

Horie¹,

Ogura²

1995

Transactions of the American Mathematical Society

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Abstract.Let k be any imaginary abelian field with conductor not exceeding 100, where an abelian field means a finite abelian extension over the rational field Q contained in the complex field. Let C(k) denote the ideal class group of k , C~(k) the kernel of the norm map from C(k) to the ideal class group of the maximal real subfield of k , and f(k) the conductor of k ; f(k) < 100 .Proving a preliminary result on 2-ranks of ideal class groups of certain imaginary abelian fields, this paper determines the structure of the abelian group C~~(k) and, under the condition that either [k : Q] < 23 or f(k) is not a prime > 71 , determines the structure of C(k).We shall mean by an abelian field a finite abelian extension over the rational

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Group-theoretic constraints on the structure of the class group

Cited by 19 publications

References 4 publications

Tame kernels of cubic cyclic fields

Tame kernels of cubic cyclic fields

On the Galois module structure of ideal class groups

On the Ideal Class Groups of Imaginary Abelian Fields with Small Conductor

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