s-半置换子群与p-幂零群

s-Semipermutable Subgroups and p-nilpotent Groups

利用Sylow子群的循环正规子群的s-半置换性得到有限群为p-幂零群的一些充分条件.

Let G be a finite gtoup.A subgroup H of a group G is called semipermutable if it is permutable with every subgroups K of G with（｜H｜,｜K｜）=1,and s-semipermutable if it is permutable with every Sylowp-subgroups of G with（p,｜G｜）=1.The influence of s-semipermutablity of subgroups of Sylow subgroup of a finite group on its p-nilpottence are investigated.