Sylow子群的极大子群皆s-半正规的有限群(英文)  

Finite Groups Whose Maximal Subgroups of Sylow Subgroups are s-seminormal

作　　者：王坤仁[1] 

机构地区：[1]四川师范大学数学与软件科学学院,四川成都610066

出　　处：《四川师范大学学报（自然科学版）》2005年第3期253-255,共3页Journal of Sichuan Normal University（Natural Science）

基　　金：四川省学位委员会;四川省教育厅重点学科建设基金资助项目

摘　　要：子群H称为在有限群G中s 半正规,若H同G的所有阶互素于｜H｜的Sylow子群可换.主要结果如下:有限群G的所有Sylow子群及其极大子群都在G中s 半正规的充要条件是G的所有阶互素的Sylow子群之极大子群互相可换并且G的每个主因子H/R是素数阶的,若｜H/R｜=p,则｜G/CG(H/R) ｜=qb,其中素数q使qb 整除p- 1 .A subgroup H of a finite group G is called s-seminormal in G if H permutes with all Sylow subgroups of G with order prime to |H|. In this paper, the structure of finite groups G with maximal subgroups of Sylow subgroups s-seminormal in G is determined:G is a group with s-seminormal Sylow subgroups and s-seminormal maximal subgroups of Sylow subgroups if and only if all maximal subgroups of Sylow subgroups of G with coprime order permute each other and each chief factor H/R of G is of prime order, moreover, if |H/R|=p then |G/C_G(H/R)|=q^b, where q is a prime and q^b divides p-1.

关 键 词：S-半正规 极大子群 SYLOW子群 超可解性 

分 类 号：O152.1[理学—数学]