Sylow p-子群的结构对有限群的Coleman外自同构群的影响

J4 ›› 2013, Vol. 48 ›› Issue (6): 5-8.

Sylow p-子群的结构对有限群的Coleman外自同构群的影响

海进科,李正兴

青岛大学数学科学学院, 山东青岛 266071

收稿日期:2012-08-06 出版日期:2013-06-20 发布日期:2013-06-09
作者简介:海进科(1964-),男，博士,教授,主要研究领域为有限群及其表示. Email:haijinke2002@yahoo.com.cn
基金资助:
国家自然科学基金资助项目(11171169; 11071155); 山东省优秀中青年科研奖励基金资助项目(BS2012SF003)

Influence of the structure of Sylow p-subgroups on Coleman outer automorphism groups of finite groups

HAI Jin-ke, LI Zheng-xing

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

Received:2012-08-06 Online:2013-06-20 Published:2013-06-09

摘要/Abstract

摘要：

设G是一个有限群,通过考虑G的Sylow p子群的结构, 证明了如果G／F*(G)无主因子同构于Cp,则G的Coleman外自同构群是p′群。

关键词: 自同构群;同调群;广义Fitting子群

Abstract:

Let G be a finite group. It is proved that if G／F*(G) has no chief factor isomorphic to Cp, then the Coleman outer automorphism group of G is a p′group by considering the structure of Sylow psubgroups of G.

Key words: automorphism group; homology group; generalized Fitting subgroup

海进科,李正兴. Sylow p-子群的结构对有限群的Coleman外自同构群的影响[J]. J4, 2013, 48(6): 5-8.

HAI Jin-ke, LI Zheng-xing. Influence of the structure of Sylow p-subgroups on Coleman outer automorphism groups of finite groups[J]. J4, 2013, 48(6): 5-8.

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