有限群的弱n-Engle条件和p-幂零性(英文)

A Weak n-Engel Condition and the p-nilpotency of Finite Groups

有限群 G的一个弱 n- Engle条件是指 :对于 G的 2个元素 x,y和某个非负整数 n,[x,ny]∈ Z(G)成立 ,如果存在 G的一个子群 K满足 H K =G和 H∩ K≤ Core G(H ) ,则 G的一个子群 H称为 c-可补的 .利用极小子群的弱 n- Engle条件和 4阶循环子群的 c-可补性 ,讨论了 G的 p-幂零性 .

Let G be a finite group.For a weak n-Engel condition of G, we mean that \∈Z(G) for two elements x and y of G,where n is a positive integer.A subgroup H of G is called c-supplemented in G if there exists a subgroup K of G such that HK=G and H∩K≤Core G(H).In this paper,we discuss the sufficient conditions of a p-nilpotent group by using supplementation of the cyclic subgroups of order 4 under some assumptions weaker than the n-Engel condition on minimal subgroups of G.