ON WEAKLY H-EMBEDDED SUBGROUPS AND p-NILPOTENCE OF FINITE GROUPS

Let G be a finite group and H a subgroup of G. We say that H is an H-subgroup of G if N-G(H) boolean AND H-g <= H for all g is an element of G; H is called weakly H-embedded in G if G has a normal subgroup K such that H-G = HK and H boolean AND K is an H-subgroup of G, where H-G is the normal clousre of H in G, i.e., H-G = < H-g vertical bar g is an element of G >. In this paper, we study the p-nilpotence of a group G under the assumption that every subgroup of order d of a Sylow p-subgroup P of G with 1 < d < vertical bar P vertical bar is weakly H-embedded in G. Many known results related to p-nilpotence of a group G are generalized.