On one property of hypercyclic groups - Chechin, S. A. (Ukrains’kyi Matematychnyi Zhurnal, 1995)
We prove that the condition of periodicity of all normal Abelian subgroups of a group with increasing normal series with cyclic factors such that infinite factors are central is preserved on passing to subgroups of finite index. We present an example which demonstrates that the requirement that all infinite cyclic factors must be central cannot be omitted.