四川师范大学学报（自然科学版）2006，Vol.29Issue(5)：505-508,4.
关于有限群的幂零性与p-幂零性的一些判别
Some Criteria for Nilpotence and p-Nilpotence of Finite Groups
摘要
Abstract
The main object of this paper is to show the following two theorems:(1) Let N be a normal subgroup of a finite group G such that G/N is p-nilpotent. If every dement of P∩Gp-N with order p or 4 (when p = 2) lies in Z(NG(P)) , where P ∈ Sylp(N) and Gp-N is the p-nilpotent residual of G,then G is p-nilpotent.(2) Let H be a normal subgorup of a finite group G such that G/H is nilpotent. If, for all prime divisors p of |H| and P ∈ Sylp (H), x is a weak left Engle element of Nc(P) for each element x of P ∩ Gp-N with order p or 4 (when p ＝2), where Gp-N is the p-nilpotent residual of G, then G is nilpotent.关键词
弱左Engle元素/幂零性/p-幂零性/p-幂零剩余Key words
Weak left Engle element/Nilpotence/p-nilpotence/p-nilpotent residual分类
数理科学引用本文复制引用
王坤仁..关于有限群的幂零性与p-幂零性的一些判别[J].四川师范大学学报（自然科学版）,2006,29(5):505-508,4.基金项目
四川省学位委员会和四川省教育厅重点学科建设基金资助项目 （）
