有限可解群的若干充分条件

运用有限群的弱c-正规性,得到了有限可解群的若干充分条件,推广了相关文献的一些结果.     

极小子群对有限群结构的影响

设Ｇ是一个有限群．Ｇ的极小子群如何影响群的结构是一个人们感兴趣的问题．在本文中,我们用极小子群的ｃ－正规的条件刻划群Ｇ的结构．我们推广了一些已知的结果．     

极大子群与p-幂零群

设G为一个群,H为G的一个子群,称H在G中是S-半置换的,若对G的任意一个Sylowp-子群Gp,只要(p,|H|)=1,就有GpH=HGp;称H在G中是c-正规的,若存在G的正规子群T使得G=HT,H∩T≤HG,其中HG是G的包含在H中的最大的正规子群。利用S-半置换子群和c-正规子群获得了p-幂零群的一个充分条件,由     

The Influence of Minimal Subgroups on the Structure of Finite Groups

Abstract Let G be a finite group. The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars. In this paper we try to use c-normal condition on minimal subgroups to characterize the structure of G. Some previously known results are generalized. The author is supported in part by NSF of China and NSF of Guangdong Province     

弱次正规子群和有限群的可解性

如果群G有次正规子群K使HK⊿⊿G且H∩K⊿⊿G,那么子群H被称做群G的弱次正规子群.利用极大子群Sylow子群或Sylow子群正规化子的子群的弱次正规性得到了一些关于有限群的可解性结论.     

每个子群都c-正规的有限群

在本文中我们研究有限CN-群, 即每个子群都c-正规的有限群. 我们得到以下结果:群G是CN-群当且仅当G^∈的每个子群都在G中正规.群G是CN-群当且仅当G可解且c-正规性是传递的.设p是一个奇素数, P是一个p-群, 则P是一个CN-群当且仅当Φ(P)≤Z(P).我们也得到了一些CN-群的直积为CN-群的判别条件.     

Finite groups with some ss-quasinormal and c-normal subgroups

Let ℱ be a saturated formation containing the class of supersolvable groups. In this paper, we use c-normal subgroups and ss-quasinormal subgroups to give criteria for a group to belong to ℱ.     

On c-Normal Subgroups of Finite Groups

A subgroup H is said to be c-normal in a group G if there exists a normal subgroup K of G such that G = HK and H K is contained in H_G, where H_G is the maximal normal subgroup of G. We determine the structures of some groups in which some primary subgroups is c-normal.AMS Mathematics Subject Classification (2000) 20D10 20D20