有限群的PCSM-子群  

Pcsm-Subgroups of Finite Groups

作　　者：李华[1,2] 钱国华[2] 

机构地区：[1]江苏大学理学院,江苏镇江212013 [2]常熟理工学院数学系,江苏常熟215500

出　　处：《青岛大学学报（自然科学版）》2008年第3期12-14,共3页Journal of Qingdao University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10571128)

摘　　要：设G是一个有限群,H为G的子群,如果对于G的任意Sylow子群的极大子群M,至少存在M的一个共轭子群Mx,x∈G,使得HMx=MxH,则称子群H为G的PCSM-子群。考察了某些子群是PCSM-子群时的有限群结构,特别地获得了超可解群的一些充分条件。A subgroup H of a group G is called PCSM-subgroup in G if there exists at least one G-conjugate of each maximal subgroup M of any Sylow subgroup of G such that HMx=MxH for some x∈G. The aim of this paper is to investigate the structure of a finite group under the assumption that certain subgroups are PCSM-subgroups. Furthermore some sufficient conditions for supersolvability are obtained.

关 键 词：PCSM-子群 极大子群 超可解 

分 类 号：O152.1[理学—数学]