The influence of M-supplemented subgroups on the structure of finite groups

A subgroup H of a group G is said to be M-supplemented in G if there exists a subgroup B of G = H B and T B < G for every maximal subgroup T of H. Moreover, a subgroup H is called c-supplemented in G if there exists a subgroup K such that G = H K and H boolean AND K <= H(G) where H(G) is the largest normal subgroup of G contained in H. In this paper we give some conditions of supersolvability of finite group under assumption that some primary subgroups have some kinds of supplements, which are generalisations of some recent results.