所有极大子群皆交换或正规的有限群  

Finite Groups Whose Maximal Subgroups are Either Abelian or Normal

作　　者：雒晓良[1] 秦鑫[1] 

机构地区：[1]吕梁学院数学系,山西离石033000

出　　处：《山西师范大学学报（自然科学版）》2011年第1期1-3,共3页Journal of Shanxi Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10771132)

摘　　要：本文研究了极大子群或者交换或者正规的有限群的结构.首先我们证明了这类群为可解群并且G/F(G)幂零.其次通过分析这类群的子群,给出了这类群的一个充要条件以及一些结构性质.The objective of this paper is to study the finite groups whose maximal subgroups are either abelian or normal.Firstly,conclusions are proved that such groups are soluable and the nilpotent length of these groups is no more than 2.Secondly,by taking into account of the Sylow subgroups,the analysis shows a necessary and sufficient condition and some structures for this kind of groups.

关 键 词：可解群 极大子群 幂零长 A-群 非幂零群 

分 类 号：O152.1[理学—数学]