The aim of this paper is to prove the following result: Let $\pi$ be a set of odd primes. If the group $G=AB$ is the product of two $\pi$-decomposable subgroups $A=A_\pi \times A_{ \pi'}$ and $B=B_\pi \times B_{ \pi'}$, then $G$ has a unique conjugacy class of Hall $\pi$-subgroups, and any $\pi$-subgroup is contained in a Hall $\pi$-subgroup (i.e. $G$ satisfies property $D_{ \pi}$).
Categories: math.GR