Finite p-Nilpotent Groups with Some Subgroups Weakly M-Supplemented

摘要

Suppose that G is a finite group and H is a subgroup of G. Subgroup H is said to be weakly M-supplemented in G if there exists a subgroup B of G such that (1) G = HB, and (2) if H-1/H-G is a maximal subgroup of H/H-G, then H1B = BH1 < G, where H-G is the largest normal subgroup of G contained in H. We fix in every noncyclic Sylow subgroup P of G a subgroup D satisfying 1 < divide D divide < divide P divide and study the p-nilpotency of G under the assumption that every subgroup H of P with divide H divide = divide D divide is weakly M-supplemented in G. Some recent results are generalized.