Geodesic
Torsion-free groups with factor-groups on their hypercenter which are periodic
Matematičeskie zametki, Tome 8 (1970) no. 3, pp. 373-383 
V. M. Kotlov. Torsion-free groups with factor-groups on their hypercenter which are periodic. Matematičeskie zametki, Tome 8 (1970) no. 3, pp. 373-383. http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a9/
@article{MZM_1970_8_3_a9,
     author = {V. M. Kotlov},
     title = {Torsion-free groups with factor-groups on their hypercenter which are periodic},
     journal = {Matemati\v{c}eskie zametki},
     pages = {373--383},
     year = {1970},
     volume = {8},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1970_8_3_a9/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Assume that $G$ is a torsion-free group, $Z_k(G)$ is the $k$-th term of the upper central series of $G$, and $\overline{G}_k=G/Z_k(G)$ is a nontrivial periodic group. Then every finite subgroup of $\overline{G}_k$ is nilpotent of class not higher than $k$; the group $k\geqslant2$ contains an infinite subgroup with $k$ generators if $\overline{G}_k$ and two generators if $k=1$. Moreover any nontrivial invariant subgroup of $\overline{G}_k$ is infinite. All elements of $\overline{G}_k$ are of odd order. This assertion is generalized.