The $D_π$-property on products of $π$-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 πdecomposable subgroups A = A π × A π ′ and B = B π × 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 D π ).