条件置换子群对有限群结构的影响

上海大学学报(自然科学版)

条件置换子群对有限群结构的影响

胡玉生;郭秀云

上海大学理学院，上海 200444

收稿日期:2006-03-02 出版日期:2007-02-28 发布日期:2007-02-28

Influence of Conditionally Permutable Subgroups on the Structure of Finite Groups

HU Yu sheng;GUO Xiu yun

School of Sciences, Shanghai University, Shanghai 200444, China

Received:2006-03-02 Online:2007-02-28 Published:2007-02-28

摘要/Abstract

摘要： 有限群G的一个子群H称为G的条件置换子群，如果对于G的任意子群T，存在x∈G，使得HT(x)=TxH.如果H是G的每个包含H的子群的条件置换子群，则称H是G的完全条件置换子群.该文主要研究了极大子群、Sylow子群的某些子群以及极小子群的条件置换性对有限群构造的影响，获得了一些新的结果.

关键词: Fitting子群, 极大子群, 条件置换子群, 完全条件置换子群

Abstract: A subgroup H of a finite group G is said to be conditionally permutable in G if for every subgroup T of G there exists an element x ∈ G such that HTx=TxH. If H is conditionally permutable in every subgroup of G containing H ,then H is said to be completely conditionally permutable subgroup in G .In this paper,some new results are obtained according to the conditional permutability of some subgroups.

Key words: completely conditionally permutable subgroups, fitting subgroups, maximal subgroups, conditionally permutable subgroups

胡玉生;郭秀云. 条件置换子群对有限群结构的影响[J]. 上海大学学报(自然科学版).

HU Yu sheng;GUO Xiu yun . Influence of Conditionally Permutable Subgroups on the Structure of Finite Groups[J]. Journal of Shanghai University（Natural Science Edition）.