On Hypercentral Groups G With |G:G n |

Abstract

In 1960, Baumslag, following up on work of Cernikov for the 1940s, proved that a hypercentral p-group G with G = G p is a divisible Abelian group. In this article, we provide an interesting generalization of this 45 year old result: If a hypercentral p-group G satisfies |G:G p |<∞ (of course, it contains G = G p ), there exists a normal divisible Abelian subgroup D such that |G:D|<∞.