有关p-幂零群的刻画(英文)

Some Characterizations of p-Nilpotency for Finite Groups

设A是G的子群,X是G的非空子集.如果A在G中存在补T,使得A与T的每个Sylow子群都X-置换,则称A在G中X-s-半置换.研究X-s-半置换性质对群的结构的影响,并得到有关p-幂零群的一些刻画.

Let A be a subgroup of group G,and X a non-empty subset of G.A is said to be X-s-semipermutable in G if A has a supplement T in G such that A is X-permutable with every Sylow subgroup of T.In this paper,the influences of X-s-semipermutability of some subgroups on the structure of finite groups are investigated.Some new criteria for group G to be p-nilpotent are obtained.