半CAP-子群与有限群的性质(英文)  

Semi CAP-subgroups and the properties of finite groups

作　　者：杨元韡[1] 黎先华[1] 

机构地区：[1]苏州大学数学科学学院,江苏苏州215006

出　　处：《苏州大学学报（自然科学版）》2008年第2期1-6,共6页Journal of Soochow University(Natural Science Edition)

基　　金：the NNSF of China(10571128);Suzhou City Senior Talent Supporting Project

摘　　要：设G是有限群,G的子群H称为G的半CAP-子群,如果存在G的一个主群列1 =G0■G1 …■Gn-1■Gn=G使得H覆盖或者避开Gi/Gi-1,其中i=1,2,…,n.本文主要讨论极小子群和4阶循环子群的半覆盖-避开性对有限群结构的影响.Let G be a finite group.A subgroup H of G is said to be a semi CAP-subgroup of G if there exists a chief series 1=G0△←G1△← …△←Gn-1△←Gn=G such that for every i=1,2,…,n,either H covers Gi/Gi-1 or H avoids Gi/Gi-1.The purpose here is to study the influence of semi cover-avoiding properties of some minimal subgroups and some cyclic subgroups of order 4 on the structure of finite groups.

关 键 词：极小子群 CAP-子群 P-幂零 群系 

分 类 号：O152.1[理学—数学]