关于正规p-补

ON NORMAL p-COMPLEMENTS

本短文得到的主要结果为:(1)设G为p-可解群,P∈Syl_p G,P循环,则G有正规p-补或GL有正规p-补.(2)设p为|G|的最小素因子,P∈Syl_pG,P正则或为Hamilton 2-群,则G有正规p-补的充要条件是对任意P的含Φ(P)且阶为p|φ(P)|的子群均在N_G(P)中类正规.

Let G be a finite group and P a Sylow p-subgroup of G.Theorem A If G is p-solvable and P is cyclic, then either G or G' has a normal p-complement.Theorem B Suppose that p is the smallest prime divisor of |G| and P is either regular or a Hamiltonian 2-group. Then G has a normal p-complement if, and only if. every subgroup of P which contains (P) and is of order is pronorma.l in NG(P).