The $$D_{\pi }$$-property on products of $$\pi $$-decomposable groups

Abstract

The aim of this paper is to prove the following result: Let π be a set of odd primes. If the group G = AB is the product of two π-decomposable subgroups A = Aπ × A π and B = Bπ × B π , then G has a unique conjugacy class of Hall π-subgroups, and any π-subgroup is contained in a Hall π-subgroup (i.e. G satisfies property Dπ).