ON WEAKLY H-SUBGROUPS OF FINITE GROUPS

Let G be a finite group. A subgroup H of G is called an H-subgroup in G if N-G(H) boolean AND H-x <= H for all x is an element of G. A subgroup H of G is called weakly H-subgroup in G if there exists a normal subgroup K of G such that G = HK and H boolean AND K is an H-subgroup in G. In this article, we investigate the structure of the finite group G under the assumption that all maximal subgroups of every Sylow subgroup of some normal subgroup of G are weakly H-subgroups in G. Some recent results are extended and generalized.