Geodesic
On various rank conditions in infinite groups
Algebra and discrete mathematics, no. 4 (2007), pp. 23-44.

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In the current survey the authors consider some of the main theorems concerning groups satisfying certain rank con- ditions. They present these theorems starting with recently estab- lished results. This order of exposition is different, indeed opposite to chronological, but it allows them to present the main develop- ment 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.
Keywords: rank, Hirsh–Zaitsev rank, special rank. 
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M. R. Dixon; L. A. Kurdachenko; I. Ya. Subbotin. On various rank conditions in infinite groups. Algebra and discrete mathematics, no. 4 (2007), pp. 23-44. http://geodesic.mathdoc.fr/item/ADM_2007_4_a3/