This article is cited in 52 papers

On recognition of finite simple groups with connected prime graph

A. V. Vasil'ev^a, I. B. Gorshkov<sup>b

a</sup> Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
^b Novosibirsk State University, Novosibirsk

Abstract: The spectrum of a finite group is the set of its element orders. We prove a theorem on the structure of a finite group whose spectrum is equal to the spectrum of a finite nonabelian simple group. The theorem can be applied to solving the problem of recognizability of finite simple groups by spectrum.

Keywords: finite group, finite simple group, spectrum of a group, prime graph of a group.

UDC: 512.542

Received: 30.10.2007

 English version: Siberian Mathematical Journal, 2009, 50:2, 233–238

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