摘要
最近几年,利用子群的置换性质刻画有限群结构成为了人们感兴趣的课题.文献(J.Algebra,2007,315:31-41.)引入了X-半置换子群的概念:设X是有限群G的一个非空子集.G的一个子群A称为在G中X-半置换,如果A在G中有一个补T使得对于T的任意子群T1,存在x∈X使得ATx1=Tx1A.结合文献(Commun.Algebra,2008,36(6):2333-2340.)引入的p-群的特殊极大子群,利用这些极大子群的X-半置换性,通过对X的巧妙选择,得到有限群成为p-可解、p-幂零和超可解的若干充分条件,推广了若干熟知的相关结果.这些新结果将丰富和促进有限群结构的相关研究.
In recent years, it has been of interest to use some permutable properties of subgroups to characterize the structure of finite groups. Guo et al (J. Algebra ,2007,315:31-41. ) introdueed the eoncept of X-semipermutable subgroups : Let X be a non-empty subset of a group G. A subgroup A of G is said to be X-semipermutable in G if A has a supplement T in G such that for every subgroup Tl of T there exists an element x E X such that ATx1=Tx1A. In this paper, by combining the special maximal subgroups of p-groups introduced by Li et al ( Commun. Algebra,2008,36 (6) :2333-2340. ) and cleverly ehoieing X, we obtain some new sufficient conditions for a finite group to be p-supersolvable, p-nilpotent and supersolvable with X-semipermutation of the special maximal subgroups of Sylow subgroups. Our results generalize some known related results, which will enrich and promote the related study of structure of finite groups.
出处
《四川师范大学学报(自然科学版)》
CAS
CSCD
北大核心
2013年第1期39-43,共5页
Journal of Sichuan Normal University(Natural Science)
基金
supported by NSF of China(10961007,11161006)
广西自然科学基金(0991101)
广西教育厅科研基金(200807LX432)资助项目~~
关键词
有限群
X-半置换
P-幂零
P-超可解
超可解
finite group
X-semipermutable
p-nilpotent
p-supersolvable
supersolvable