ヒルベルト類体の分解について

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概要

• 論文の詳細を見る

• Let k be a number field and K a finite Galois extension of k. Let G be the Galois group of K over k and K' the Hilbert class field of K. Then K' is a Galois extension of k. Let H = G(K'/K) and E = G(K'/k). We have the group extension: [numerical formula] We will denote this group extension by E(K/k) and are interesting in the problem of when E(K/k) splits. We have the subfield of K over k whose Galois group over k is isomorphic to the p-Sylow subgroup of G when G is an abelian group. We will denote this subfield of K by K_p. In Section 1, we will give a field theoretic characterization for E(K/k) to split when G is a cyclic group. In Section 2, we will prove that E(K/k) splits if E(K_p/k) splits for all p-Sylow subgroups of G when G is an abelian group. In Section 3, we will prove that E(K/k) splits if and only if E(K_p/k) splits for all p-Sylow subgroups of G when K is an unramified cyclic extension of k.

• 明治大学の論文

著者

• 稲富 彬

  Department Of Mathematic School Of Science And Technology Meiji University

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