The mixability conjecture for finite groups

Let $G$ be a finite group. The mixability conjecture. $G$ is mixable if and only if it has no nontrivial quotients of odd order. This claims that the obstruction given by nontrivial odd-order quotients is the only obstruction to mixability; in particular, all finite simple groups should be mixable. The paper establishes that groups with a nontrivial quotient of odd order are not mixable and proves mixability for several families, but the converse remains open.