弱C-正规子群与p-幂零群

Weakly C-normal Subgroups and p-nilpotent Groups

称群G的一个子群H为弱C-正规的,如果存在G的次正规子群K,使得G=HK且H∩K≤HG,其中HG表示G包含在H中的最大的正规子群.利用子群的弱C-正规性得到有限群成为p-幂零群的一些充分条件.

A subgroup H of a group G is said to be weakly C-normal if there exists a subnormal group K of G such that G = HK and H∩K〈HG where HG is the maximal normal subgroup of G contained in H. In this paper, in terms of weakly C-normality of subgroups, some sufficient conditions for a finite group to be p-nilpotent are obtained.