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

Abstract.

In this paper, we get the main theorem: Let p be a prime dividing the order of G and $G = P \cdot H$, where $P \in {\rm Syl}_p(G)$ 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) $N_G(P)/C_G(P)$ 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.