有限群的CAP-子群与π-可解性  

CAP-subgroups and π-solvability of Finite Groups

作　　者：黄杰山[1] 

机构地区：[1]南宁职业技术学院计算机与信息工程系,广西南宁530012

出　　处：《广西师范学院学报（自然科学版）》2006年第3期5-7,共3页Journal of Guangxi Teachers Education University(Natural Science Edition)

摘　　要：有限群G的子群A称为在G中具有复盖-远离性质(或G的CAP-子群),若对于G的任意主因子H/K,HA=KA或者H∩A=K∩A.该文利用Hall子群的复盖-远离性质,得到有限群可解和π-可解的若干充分及必要条件,推广了几个已知的定理.A subgroup A of a finite group G is said to have the cover - avoidance property in G or be a CAP-subgroup of G if for every chief factor H/K of G, either HA = KA or H∩ A = K ∩A. By using the cover-avoidance properties of some Hall subgroups, we present several sufficient for a finite group to be solvable and π-solvable. Our results generlize some known theorems.

关 键 词：有限群 HALL子群 CAP-子群 可解群 Π-可解群 

分 类 号：O152.1[理学—数学]