On characterisation of a finite group by the set of conjugacy class sizes

2019/12/16 by Gorshkov, Ilya
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1912.07206

Abstract

Let G be a finite group and N(G) be the set of its conjugacy class sizes. In the 1980's Thompson conjectured that the equality N(G)=N(S), where Z(G)=1 and S is simple, implies the isomorphism G≃ S. In a series of papers of different authors Thompson's conjecture was proved. In this paper, we show that in some cases it is possible to omit the conditions Z(G)=1 and S is simple and prove a more general result.

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