【摘 要】
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The norm N(G) of a group G is the intersection of normalizers of all the subgroups of G. Let G be a finite group, p a prime dividing the order of G, and P a Syl
【机 构】
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Department of Mathematics, Shanghai University, Shanghai 200444, China
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The norm N(G) of a group G is the intersection of normalizers of all the subgroups of G. Let G be a finite group, p a prime dividing the order of G, and P a Sylow p-subgroup of G. In this paper, it is proved that G is p-nilpotent if Ω1(P)≤N(NG(P)),and when p = 2, Ω2(P) = .Some applications of this result are given. Finally, a class of finite p-groups in which the index of the norm is exactly p is described.
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