On Completely C-permutability of Maximal Subgroups of Sylow Subgroups

Subgroups H of group G is completely conditionally permutable in G if for every subgroup T of G there exists an element x∈〈H,T〉 such that HT~x=T~xH.In this paper, we give some conclusions for supersolubility of groups by using the completely c-permutability of maximal subgroups of Sylow subgroups:① Let G be a solvable group, if every maximal subgroup of Sylow subgroups of G is completely c-permutable in G, then G is supersoluble;② Let F be a saturated formation containing U.Suppose that G is group with a solvable normal subgroup N such that G/N∈F.If every maximal subgroup of Sylow subgroups of N is completely c-permutable in G, then G∈F.