子群的CAP_(S_(p)^(*))性质对主因子结构的影响  

Influence of the CAP_(S_(p)^(*))properties of subgroups on the structure of chief factors

作　　者：王鸿志 缪龙 刘威 WANG Hongzhi;MIAO Long;LIU Wei(College of Science,Hohai University,Nanjing 210098,China;School of Mathematical Sciences,Yangzhou University,Yangzhou 225002,Jiangsu,China)

机构地区：[1]河海大学理学院,南京210098 [2]扬州大学数学科学学院,江苏扬州225002

出　　处：《华中师范大学学报（自然科学版）》2024年第3期304-309,共6页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11871062);江苏省自然科学基金项目(BK20181451);中俄国际合作项目NSFC-RFBR(12011530061).

摘　　要：称子群A为群G的CAP_(S_(p)^(*))-子群,若G的任意pd-主因子H/K满足AH=AK或|A∩H:A∩K|p≤p.该文探究极大子群、二极大子群以及Sylow子群的CAP_(S_(p)^(*))性质对群的主因子结构的影响,并给出相关的刻画.A subgroup A is called a CAP_(S_(p)^(*))-subgroup of a finite group G,if for any pd-chief factor H/K of G,we have either AH=AK or|A∩H:A∩K|p≤p.In this paper,the influence of the CAP_(S_(p)^(*))properties of maximal subgroups,second maximal subgroups and Sylow subgroups on the structure of chief factors of finite groups is explored,and the related characterizations are given.

关 键 词：主因子 极大子群 二极大子群 SYLOW子群 CAP_(S_(p)^(*))-子群 

分 类 号：O152.1[理学—数学]