四川师范大学学报（自然科学版）2013，Vol.36Issue(1)：39-43,5.DOI:10.3969/j.issn.1001-8395.2013.01.008
具有某些X-半置换子群的有限群
Finite Groups with Some X-semipermutable Subgroups
摘要
Abstract
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.) introduced the concept of X-semiper-mutable 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 T1 of T there exists an element x ∈ 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 choicing 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 generahze some known related results,which will enrich and promote the related study of structure of finite groups.关键词
有限群/X-半置换/p-幂零/p-超可解/超可解Key words
finite group/ X-semipermutable/ p-nilpotent/ p-supersolvable/supersolvable分类
数理科学引用本文复制引用
卢若飞,韦华全,董淑琴,孙旭..具有某些X-半置换子群的有限群[J].四川师范大学学报（自然科学版）,2013,36(1):39-43,5.基金项目
国家自然科学基金(10961007、11161006)、广西自然科学基金(0991101)和广西教育厅科研基金(200807LX432)资助项目 （10961007、11161006）
This work is supported by NSF of China (10961007,11161006) （10961007,11161006）
