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Israel Journal of Mathematics

, Volume 51, Issue 1–2, pp 125–150 | Cite as

Solubility of finite groups admitting a fixed-point-free automorphism of orderrst III

  • Peter Rowley
Article

Abstract

This paper, which is one of a series of four, contributes to the proof of the following

Theorem.A finite group admitting a coprime fixed-point-free automorphism α of order rst (r, s andt distinct primes)is soluble.

Here we prove that in a minimal counterexample to the above theorem the set ofα-invariant Sylowp-subgroupsP, such thatC p(α i)≠1 for allα i≠1, generate a soluble subgroup.

Keywords

Finite Group Sylow Subgroup Invariant Subgroup Characteristic Subgroup Require Contradiction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Z. Arad and G. Glauberman,A characteristic subgroup of a group of odd order, Pac. J. Math.56(2) (1975), 305–319.MATHMathSciNetGoogle Scholar
  2. 2.
    D. Gorenstein,Finite Groups, Harper and Row, New York, 1968.MATHGoogle Scholar
  3. 3.
    P. J. Rowley,Solubility of finite groups admitting a fixed-point-free automorphism of order rst I, Pac. J. Math.193 (1981), 201–235.MathSciNetGoogle Scholar
  4. 4.
    P. J. Rowley,Solubility of finite groups admitting a fixed-point-free automorphism of order rst II, J. Algebra83 (1983), 293–348.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University 1985

Authors and Affiliations

  • Peter Rowley
    • 1
  1. 1.Department of MathematicsUMISTManchesterEngland

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