On groups of finite rank

Abstract

We study the structure of groups of finite (Prüfer) rank in a very wide class of groups and also of central extensions of such groups. As a result we are able to improve, often substantially, on a number of known numerical bounds, in particular on bounds for the rank (resp.\ Hirsch number) of the derived subgroup of a group in terms of the rank (resp.\ Hirsch number) of its central quotient and on bounds for the rank of a group in terms of its Hirsch number.