关于有限群Coleman自同构的一个注记

doi:10.6040/j.issn.1671-9352.0.2015.587

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (4): 35-38.doi: 10.6040/j.issn.1671-9352.0.2015.587

关于有限群Coleman自同构的一个注记

海进科,王伟,何威萍

青岛大学数学科学学院, 山东青岛 266071

收稿日期:2014-12-25 出版日期:2016-04-20 发布日期:2016-04-08
作者简介:海进科(1964— ),博士,教授,研究方向为有限群及其表示. E-mail:haijinke2002@aliyun.com
基金资助:
国家自然科学基金资助项目(11171169)

A note on Coleman automorphisms of finite groups

HAI Jin-ke, WANG Wei, HE Wei-ping

College of Mathematics, Qingdao University, Qingdao 266071, Shandong, China

Received:2014-12-25 Online:2016-04-20 Published:2016-04-08

摘要/Abstract

摘要： 设G为有限群,KG且K为非交换单群,若G/K为交换群或非交换单群, 则G的每个Coleman自同构为内自同构,即Out_Col(G)=1。特别地,这样的有限群G具有正规化子性质。

关键词: 非交换单群, 正规化子问题, Coleman自同构

Abstract: Let K be a normal subgroup of a finite group G and K be a non-abelian simple group. If G/K is a abelian group or a non-abelian simple group. It is shown that every Coleman automorphism of G is an inner automorphism, that is, Out_Col(G)=1. In particular, the normalizer property holds for G.

Key words: non-abelian simple groups, the normalizer problem, Coleman automorphisms

中图分类号:

O152.6

海进科,王伟,何威萍. 关于有限群Coleman自同构的一个注记[J]. 山东大学学报（理学版）, 2016, 51(4): 35-38.

HAI Jin-ke, WANG Wei, HE Wei-ping. A note on Coleman automorphisms of finite groups[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(4): 35-38.

参考文献

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关于有限群Coleman自同构的一个注记

A note on Coleman automorphisms of finite groups

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