摘要
利用覆盖-远离子群的概念研究了群的超可解性和幂零性.首先利用有限群G的Fitting子群和Sylow子群的覆盖-远离性质给出了关于G超可解的几个充分条件;然后再对G的Sylow子群的正规化子等的覆盖-远离性质进行讨论,得到了关于G幂零的几个充要条件和充分条件.
The supersolvablity and nilpotency of the finite group G are characterized using the concept of cover-avoiding subgroups. First, some sufficient conditions for supersolvability of the finite group G are given, using the cover-avoiding properties of Fitting subgroup and Sylow subgroups of G. Then, the nilpotency of G is discussed and some sufficient and neccesary conditions are obtained under the assumption that the normalizers of Sylow subgroups of G have the cover-avoiding properties.
出处
《西南大学学报（自然科学版）》
CAS
CSCD
北大核心
2008年第10期1-6,共6页
Journal of Southwest University(Natural Science Edition)
基金
国家自然科学基金资助项目(10771172)
关键词
覆盖-远离子群
极大子群
超可解群
幂零群
cover-avoiding subgroup
maximal subgroup
supersolvable group
nilpotent group
