Research ArticleNo Access

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

Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

Saint Petersburg State University, Saint Petersburg, Russia

https://doi.org/10.1142/S0219498822502267Cited by:3 (Source: Crossref)

Abstract

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 $G ≃ S$ . 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.

Communicated by E. P. Vdovin

Keywords:

AMSC: 20E45

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