ABSTRACT
In Chapter 4 the discussion centers around the various types of ranks associated with groups. This ties in with some of the work in the earlier chapters. The very strong structural results of M. I. Kargapolov for locally finite groups are given. For non-periodic groups the 0-rank is also important. The work of A. I. Maltsev on torsion-free locally nilpotent groups whose abelian subgroups have finite 0-rank is described together with some of its consequences. The various connections between the different ranks is discussed. Locally finite groups with finite section rank are studied in Section 4.4 where the work of V. V. Belyaev on this issue is stated. Results are given in cases when certain systems of subgroups satisfy the various rank conditions. The powerful workof R. Baer and H. Heineken appears here as does the fundamental work of M. I. Kargapolov concerning soluble groups whose abelian subgroups have finite special rank. V. P. Shunkov obtained results of a similar nature for locally finite groups. Although most of the chapter is concerned with subgroups possessing certain properties there is some discussion of groups whose factor groups satisfy certain rank condition properties.
