Periodic residually finite groups with abelian subgroups of finite ranks. (Q291234)

This paper deals with the structure of periodic groups satisfying some further finiteness conditions. Among other results, it is proved that if \(G\) is a periodic group whose \(2\)-generator subgroups are soluble, then \(G\) has finite rank if and only if all its abelian subgroups have finite rank. Recall here that a group \(G\) is said to have finite rank if there exists a positive integer \(r\) such that every finitely generated subgroup of \(G\) can be generated by at most \(r\) elements.