On δ-permutability of maximal subgroups of Sylow subgroups of finite groups

摘要

In this paper, we get the main theorem: Let p be a prime dividing the order of G and G = P ·HG = P cdot H, where P Î Syl_p(G)P in {rm Syl}_p(G) and H is p ′-Hall subgroup of G. Let δ be a complete set of Sylow subgroups of H. If G satisfies the following conditions: i) N_G(P)/C_G(P)N_G(P)/C_G(P) is a p-group; ii) for any maximal M of P, M is δ-permutable in H, then G is p-nilpotent. Some known results are generalized.