设G是有限群,P是G的Sylow p-子群,其中p是一个素数.用NG(P)的p-幂零性及P的一些子群在G中c*-正规,研究群G的p-幂零性,得到了:(1)对于素数p,如果G的阶数与p-1互素,那么G是p-幂零群当且仅当G有某个Sylow p-子群P及一个大于1且小于|P|的自然数d,使得P的所有d阶或4阶(当d=2时)的子群在G中c*-正规；(2)如果p是奇素数,则G是p-幂零群当且仅当NG(P)是p-幂零群,并且P有子群D满足1＜| D |＜|P|及P的所有阶为|D|的子群H在G中c*-正规.%Let G be a finite group and P a Sylow p-subgroup of G, where p ε -π(G). In this paper, the p-nilpotence of G is investigated while NG(P) is p-nilpotent and some subgroups of P are c' -normal in G. The main results are as follows; (1) If(∣ G∣ ,p - 1 ) = 1 ,then G is js-nilpotent if and only if there exist a Sylow p-subgroup P and a natural number d with 1 < d < ∣ p∣ , and all subgroups of P of order d or 4 (if d -2 ) are c* -normal in G; (2) If p is an odd prime,then G is p-nilpotent if and only if NC(P) is ja-nilpotent and P has a subgroup D with 1 < | D | < ∣ P∣ such that all subgroups of P of order | D are c* -normal in G.
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