On connection between the structure of a finite group and the properties of its prime graph

被引：83
作者：
Vasil'ev, AV
机构：
[1] Sobolev Institute of Mathematics,
来源：
SIBERIAN MATHEMATICAL JOURNAL | 2005年 / 46卷 / 03期
基金：
俄罗斯基础研究基金会;
关键词：
finite group; finite simple group; prime graph of a finite group; spectrum of a group; recognition by spectrum;
D O I：
10.1007/s11202-005-0042-x
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
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.
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页码：396 / 404
页数：9
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