On various rank conditions in infinite groups

Abstract

In the current survey the authors consider some of the main theorems concerning groups satisfying certain rank conditions. They present these theorems starting with recently established results. This order of exposition is different, indeed opposite to chronological, but it allows them to present the main development of the theory. They illustrate the connections between the different ranks emphasizing, in particular, the connection between the special rank and the Hirsch–Zaitsev rank.