Finite group with given c-permutable subgroups

Abstract

Following [1] we say that subgroups H and T of a group G are c-permutable in G if there exists an element x ∈ G such that HTˣ = TˣH. We prove that a finite soluble group G is supersoluble if and only if every maximal subgroup of every Sylow subgroup of G is c-permutable with all Hall subgroups of G.