关于极大子群的指数复合  

On the Index Complex of a Maximal Subgroup

作　　者：王晓静[1] 张艳[1] 郭洪霞[2] 

机构地区：[1]北京建筑工程学院基础部,北京100044 [2]烟台师范学院数学与信息科学学院,烟台264025

出　　处：《北京建筑工程学院学报》2004年第1期81-83,80,共4页Journal of Beijing Institute of Civil Engineering and Architecture

摘　　要：利用Deskins在 195 9年所定义的有限群的极大子群的指数复合 ,给出了有限群为π -可解 ,可解 ,超可解 。By using the concept of index complex of a maximal subgroup introduced by Deskins in 1959, some new results on the solvability and supersolvability of a finite group are obtained. The main results are as follows: (1) Let F′ G={M∶M be any maximal subgroup of a finite group G, which contains some normalizer of a Sylow subgroup of G ,and ｜G∶M｜is composite},the following are equivalent: (i) G is solvable; (ii) for each M∈F′ G, there exites a maximal completion C such that for any x∈G, C xM, and C/K(C) is nilpotent; (ⅲ) for each M∈F′ G, there exites a maximal completion C such that C/K(C) is abelian or G=CM and C/K(C) is of square-free order. (2) G is supersolvable if and only if for each M∈F′ G, there exites a maximal completion C such that G=CM and C/K(C) is of square-free order.

关 键 词：极大子群 指数复合 有限群 幂零 充要条件 

分 类 号：O152.1[理学—数学]