Аn example of the $G$-periodic torsion free group

A group $G$ is called $G$-periodic if for any element $g$ of $G$ there exist the elements $h_1, h_2, \dots, h_k$ such that
$$ (h_1^{-1}gh_1)(h_2^{-1}gh_2)\dots(h_k^{-1}gh_k)=1. $$
In this note an example of $G$-periodic torsion free group is constructed.

Received: 10.04.1967