NOTE ON HILBERT-SPEISER NUMBER FIELDS AT A PRIME ＄p＄
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概要
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Let ＄p＄ be a prime number. A number field ＄F＄ satisfies the Hilbert-Speiser condition ＄(H_{p})＄ when any tame cyclic extension ＄N/F＄ of degree ＄p＄ has a normal integral basis. We show that ＄F＄ satisfies ＄(H_{p})＄ only when ＄F¥cap Q(¥zeta_{p})=Q＄ under some assumption on ＄p＄ .
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