Hilbert-Speiser number fields and the complex conjugation

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Abstract

Let <I>p</I> be a prime number. We say that a number field <I>F</I> satisfies the condition (<I>H<SUB>p</SUB></I>) when any tame cyclic extension <I>N</I>⁄<I>F</I> of degree <I>p</I> has a normal integral basis. We determine all the CM Galois extensions <I>F</I>⁄<B><I>Q</I></B> satisfying (<I>H<SUB>p</SUB></I>) for the case <I>p</I>≥5, using the action of the complex conjugation on several objects associated to <I>F</I>.

Journal

  • Journal of the Mathematical Society of Japan

    Journal of the Mathematical Society of Japan 62(1), 83-94, 2010-01-01

    The Mathematical Society of Japan

References:  24

Codes

  • NII Article ID (NAID)
    10026998840
  • NII NACSIS-CAT ID (NCID)
    AA0070177X
  • Text Lang
    ENG
  • Article Type
    ART
  • ISSN
    00255645
  • NDL Article ID
    10529924
  • NDL Source Classification
    ZM31(科学技術--数学)
  • NDL Call No.
    Z53-A209
  • Data Source
    CJP  NDL  J-STAGE 
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