4.18 (1973)

Characterize the classes $\mathfrak{K}$ of groups, meeting the following requirements: subgroups, epimorphic images and groups of automorphisms of $\mathfrak{K}$-groups are $\mathfrak{K}$-groups, but not every countable group is a $\mathfrak{K}$-group. Note that the class of all finite groups and the class of all almost cyclic groups meet these requirements.