S-拟正规嵌入子群与有限群的p-幂零性

The S-Quasinormally Embedded Subgroups and p-Nilpotency of Finite Groups

设H是有限群G的子群.如果H的Sylow子群也分别是G的某个S-拟正规子群的Sylow子群,则称H在G中S-拟正规嵌入.利用子群的S-拟正规嵌入性给出了有限群为p-幂零群的一个充分条件,推广了已有的结论.

A subgroup H of a group G is said to be S-quasinormally embedded in G,if every Sylow subgroup of H is also a Sylow subgroup of some S-quasinorml subgroup of G.In this paper,a sufficient condition for p-nilpotent groups have been obtained based on the assumption that some subgroups are S-quasinormal embedded.Our theorem is a generalization of the known results.