【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.更多还原

【Abstract】 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.更多还原