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Siberian Mathematical Journal

, Volume 56, Issue 3, pp 541–548 | Cite as

On finite soluble groups with almost fixed-point-free automorphisms of noncoprime order

  • E. I. KhukhroEmail author
Article

Abstract

It is proved that if a finite p-soluble group G admits an automorphism φ of order p n having at most m fixed points on every φ-invariant elementary abelian p′-section of G, then the p-length of G is bounded above in terms of p n and m; if in addition G is soluble, then the Fitting height of G is bounded above in terms of p n and m. It is also proved that if a finite soluble group G admits an automorphism ψ of order p a q b for some primes p and q, then the Fitting height of G is bounded above in terms of |ψ| and |C G (ψ)|.

Keywords

finite soluble group automorphism p-length Fitting height 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.University of LincolnLincolnUK

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