Outer automorphism groups of finite p-nilpotent groups

被引：0

作者：

Jin, P ^{[1
]}

机构：

[1] Shanxi Univ, Dept Math, Taiyuan 030006, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2002年 / 30卷 / 09期

关键词：

D O I：

10.1081/AGB-120013324

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

When does a finite group possess a non-trivial outer automorphism? In this paper for a finite p-nilpotent group G we shall prove the following results. (a) If \O-p(G)\ > p, then p divides the order of Out(G). (b) If O-p(G) is non-abelian, then p divides the order of C-Out(G) (Z(G)). Our results extend a famous theorem of Gaschutz and can be applied to the investigation of finite complete groups.

引用

页码：4369 / 4375

页数：7

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