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

摘要

Let G be a finite group and N(G) be the set of its conjugacy class sizes. In the 1980s, Thompson conjectured that the equality N(G) = N(S), where Z(G) = 1 and S is simple, implies the isomorphism G similar or equal to 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.