4.16 (1973)

Suppose that $\mathfrak{K}$ is a class of groups meeting the following requirements: 1) subgroups and epimorphic images of $\mathfrak{K}$-groups are $\mathfrak{K}$-groups; 2) if the group $G = UV$ is the product of $\mathfrak{K}$-subgroups $U$ and $V$ (neither of which need be normal), then $G \in \mathfrak{K}$. If $\pi$ is a set of primes, then the class of all finite $\pi$-groups meets these requirements. Are these the only classes $\mathfrak{K}$ with these properties?