One-prime power hypothesis for conjugacy class sizes

Document Type : Research Paper

Authors

1 University of East Anglia

2 Fitzwilliam College, University of Cambridge

Abstract

A finite group $G$ satisfies the on-prime power hypothesis for conjugacy class sizes if any two conjugacy class sizes $m$ and $n$ are either equal or have a common divisor a prime power. Taeri conjectured that an insoluble group satisfying this condition is isomorphic to $S \times A$ where $A$ is abelian and $S \cong PSL_2(q)$ for $q \in {4,8}$. We confirm this conjecture.

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References

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International Journal of Group Theory
Volume 6, Issue 3 - Serial Number 3
September 2017
Pages 13-19

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History

  • Receive Date: 02 November 2015
  • Revise Date: 18 December 2015
  • Accept Date: 18 December 2015
  • Published Online: 01 September 2017

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