Name: The Genus Field and Genus Number in Algebraic Number Fields
Creator: Furuta, Yoshiomi
Keywords: finite normal extension, genus field, ramification index, Galois theory, 12.50, genus number, 12.40, Class numbers, class groups, discriminants, maximal abelian subfield, 16. Peace & justice

The genus field and genus number in algebraic number fields

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Mar 1967 English Publisher:Cambridge University Press (CUP)Journal:Nagoya Mathematical Journal, volume 29, pages 281-285 (issn: 0027-7630, eissn: 2152-6842,

Authors: Furuta, Yoshiomi;

doi: 10.1017/s0027763000024387

The Genus Field and Genus Number in Algebraic Number Fields

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Abstract

Let k be an algebraic number field and K be its normal extension of finite degree. Then the genus field K* of K over k is defined as the maximal unramified extension of K which is obtained from K by composing an abelian extension over k2). We call the degree (K*: K) the genus number of K over k.

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Kanazawa University
Japan

Keywords

finite normal extension, genus field, ramification index, Galois theory, 12.50, genus number, 12.40, Class numbers, class groups, discriminants, maximal abelian subfield

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