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Archiv der Mathematik

, Volume 112, Issue 1, pp 1–3 | Cite as

A sufficient condition for fixed points of a coprime action to have a normal complement

  • M. Yasir KızmazEmail author
Article
  • 61 Downloads

Abstract

Let A be a finite group acting on a finite group G via automorphisms. Assume that \((|A|,|G|)=1\). We prove that if \(C_G(A)\) is a Hall \(\pi \)-subgroup of G, then G has a normal \(\pi \)-complement.

Keywords

Coprime action Normal complement 

Mathematics Subject Classification

20D10 20D20 

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Notes

Acknowledgements

The author would like to thank an anonymous referee for many invaluable suggestions on the original manuscript.

References

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    Isaacs, I.M.: Finite Group Theory. Graduate Studies in Mathematics, vol. 92. American Mathematical Society, Providence (2008)Google Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsMiddle East Technical UniversityAnkaraTurkey

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