13.64 (1995)

Let $\pi_e(G)$ denote the set of orders of elements of a group $G$. A group $G$ is said to be an $OC_n$-group if $\pi_e(G) = \{1, 2, \dots, n\}$. Is every $OC_n$-group locally finite? Do there exist infinite $OC_n$-groups for $n \geqslant 7$?