# On Connection Between the Structure of a Finite Group and the Properties of Its Prime Graph

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## Abstract

It is shown that the condition of nonadjacency of 2 and at least one odd prime in the Gruenberg-Kegel graph of a finite group *G* under some natural additional conditions suffices to describe the structure of *G*; in particular, to prove that *G* has a unique nonabelian composition factor. Applications of this result to the problem of recognition of finite groups by spectrum are also considered.

### Keywords

finite group finite simple group prime graph of a finite group spectrum of a group recognition by spectrum## Preview

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