s＊-半置换子群与有限群的p-幂零性

s~＊-Semipermutable Subgroups and the p-Nilpotency of Finite Groups

群G的子群H称为在G中s*-半置换,若对任意的p||G|,只要(p,|H|)=1,就存在P∈Sylp(G),使得HP=PH.利用子群的s*-半置换性给出了一个群为幂零群或p-幂零群的若干充分条件.

A subgroup H of a group G is said to s＊-semipermutable in G if there exists a Sylow p-subgroup P of G with（p,｜H｜）=1 such that HP=PH for every p∈π（G）.With s＊-semipermutable subgroups,some sufficient conditions of nilpotent and p-nilpotent group are obtained in this paper.