FINITE GROUPS WITH S-PERMUTABLE n-MAXIMAL SUBGROUPS

被引：3
|
作者：
Qian, Guohua [1 ]
机构：
[1] Changshu Inst Technol, Dept Math, Changshu 215500, Jiangsu, Peoples R China
来源：
COMMUNICATIONS IN ALGEBRA | 2015年 / 43卷 / 12期
关键词：
Finite group; n-Maximal subgroup; S-Permutable subgroup; Supersolvable group; MINIMAL SUBGROUPS;
D O I：
10.1080/00927872.2014.974102
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let G be a finite group and M-n(G)be the set of n-maximal subgroups of G, where n is an arbitrary given positive integer. Suppose that M-n(G) contains a nonidentity member and all members in M-n(G) are S-permutable in G. Then any of of the following conditions guarantees the supersolvability of G: (1) M-n(G) contains a nonidentity member whose order is not a prime; (2) all nonidentity members in M-n(G) are of prime order, and all cyclic members in Mn-1(G) of order 4 are S-permutable in G.
引用
收藏
页码：5183 / 5194
页数：12
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