6.1 (1978)

A subgroup $H$ of an arbitrary group $G$ is said to be C-closed if $H = C^2(H) = C(C(H))$, and weakly C-closed if $C^2(x) \leqslant H$ for any element $x$ of $H$. The structure of the finite groups all of whose proper subgroups are $C$-closed was studied by Gaschütz. Describe the structure of the locally finite groups all of whose proper subgroups are weakly $C$-closed.