Abelian groups admitting fixed-point-free automorphisms of order qn

  • S. V. Larin
Article
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Abstract

For a wide class of Abelian groups, necessary and sufficient conditions under which a group admits an automorphism of order qn are found; we also present necessary and sufficient conditions under which a group admits an automorphism ϕ of order qn such that ϕqm is a fixed-point-free automorphism for some m < n.

Keywords

Abelian Group Wide Class 

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Literature cited

  1. 1.
    M. M. Glukhov and S. V. Larin, “Abelian and metabelian groups with regular automorphisms and semi-automorphisms,” Mat. Zametki,12, No. 6, 727–738 (1972).MathSciNetGoogle Scholar
  2. 2.
    L. Fuchs, Infinite Abelian Groups, Vol. 1, Academic Press (1970).Google Scholar
  3. 3.
    M. I. Kargapolov and Yu. I. Merzlyakov, Foundations of the Theory of Groups [in Russian], Nauka, Moscow (1972).Google Scholar

Copyright information

© Plenum Publishing Corporation 1977

Authors and Affiliations

  • S. V. Larin
    • 1
  1. 1.Krasnoyarsk State Pedagogical InstituteUSSR

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