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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