Abstract: Planetary Journal of Social Sciences & Humanities Research

Abstract:
We say that G=AB is the mutually permutable product of the subgroups A and B if A permutes with every subgroup of B and B permutes with every subgroup of A. We say that the product is totally permutable if every subgroup of A permutes with every subgroup of B. In this paper we prove the following theorem Let G=AB be the mutually permutable product of the supersoluble subgroups A and B. If CoreG(A∩B)=1, then G is supersoluble.