摘要
群G的子群H称为在G中共轭置换,若HgH=HHg对任意的g∈G成立.本文利用共轭置换子群的概念研究了群的幂零性和超可解性的问题,获得了一个群为幂零群或超可解群的几个等价条件和充分条件.
A subgroup H of a group G is called conjugate-permutable in G if it is permutable with every conjugate subgroups Hg of H for all g∈G.In this paper,the influences of conjugate permutability on nilpotency and supersolvability of finite groups are investigated.Some equivalent and sufficient conditions for a group to be nilpotent and supersolvable are obtained.
出处
《淮阴师范学院学报（自然科学版）》
CAS
2009年第3期173-176,共4页
Journal of Huaiyin Teachers College;Natural Science Edition
基金
国家自然科学基金项目(10571128
10871032)
江苏省自然科学资助项目(BK2008156)
关键词
共轭置换子群
极小非幂零群
幂零群
超可解群
conjugate-permutable subgroup
minimal non-nilpotent group
nilpotent group
supersolvable group
