子群的半覆盖-远离性与有限群的可解性  

Semi Cover-avoidance Properties of Subgroups and Solvability of Finite Groups

作　　者：韦华全[1] 谷伟平[1] 黄杰山[2] 刘秀[3] 

机构地区：[1]广西师范学院数学科学学院,广西南宁530023 [2]南宁职业技术学院,广西南宁530022 [3]昭通师范高等专科学校数学系,云南昭通657000

出　　处：《南昌大学学报（理科版）》2009年第3期224-226,共3页Journal of Nanchang University(Natural Science)

基　　金：国家自然科学基金资助项目(10871210);广西自然科学基金资助项目(0991101);广西教育厅科研基金;广西研究生教育创新计划项目

摘　　要：有限群G的子群H称为在G中具有半覆盖-远离性质,若存在G的一个主群列1=G0<G1<…<Gl=G,使得对每一i=1,…,l,或者H覆盖主因子Gj/Gj-1或者H远离Gj/Gj-1。该文利用Hall子群的半覆盖-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,包括Schur-Zassenhaus定理。A subgroup H of a finite group G is said to have the semi cover - avoidance property in a group G if there is a chief series 1 = G0 〈 G1 〈… 〈 Gl = G, such that for every i = 1,...,l, either H covers Gj/Gj-1 or H avoids Gj/ Gj- 1. By using the semi cover - avoidance properties of some Hall subgroups, we present several sufficient conditions for a finite group to be solvable and π - solvable. Our results generlize some known theorems, including Schur - Zassenhaus theorem.

关 键 词：有限群 HALL子群 半覆盖-远离子群 可解群 Π-可解群 

分 类 号：O152[理学—数学]