有限群为超可解群的一个充要条件  

A NECESSARY AND SUFFICIENT CONDITION FOR A FINITE GROUP TO BE SUPERSOLVABLE

作　　者：王彩云[1] 张玉珠[2] 

机构地区：[1]山西大学数学系 [2]山西经济管理学院

出　　处：《山西大学学报（自然科学版）》1992年第4期332-334,共3页Journal of Shanxi University(Natural Science Edition)

摘　　要：本文证明了有限群为超可解群的一个充要条件,结果是:有限群G为超可解群当且仅当G有一个正规π-Hall子群N,且满足 (1)N是幂零群,G/N超可解, (2)存在素数P|N|,以及G的超可解子群K。The purpose of this paper is to prove a necessary and sufficient condition for a finite group to be supersolvable. The result is as follows:A finite group G is a supersolvable group if and only if there exists a normal π-Hall subgroup N in G, satisfies the following two conditions (1) N is a nilpotent group, and G/N is supersolvable,(2) There exists a prime pl |N| and a supersolvable subgroup K in G which satisfy [G:N]=P.

关 键 词：超可解群 正规群列 有限群 

分 类 号：O152.1[理学—数学]