6.29 (1978)

Suppose that a finite group $A$ is isomorphic to the group of all topological automorphisms of a locally compact group $G$. Does there always exist a discrete group whose automorphism group is isomorphic to $A$? This is true if $A$ is cyclic; the condition of local compactness of $G$ is essential (R. J. Wille, Indag. Math., 25, no. 2 (1963), 218–224).