Abelian groups

The present, fourth survey of review articles on Abelian groups includes works reviewed in the years 1979–1984. Also, as in the preceding surveys, no attention has been given to questions involving finite Abelian groups, topological groups, ordered groups, group algebras, modules, or the structure of subgroups, or to questions connected with logic. The word group throughout is understood to mean Abelian group (except in the case of the group of automorphisms of an Abelian group). Concepts and notation not defined in this survey can be found in the books [117, 118]. The letterZ throughout denotes the group (or ring) of integers,Q the group (or field) of rational numbers,Q_p the group (ring) of all rational numbers whose denominator is not divisible by the primep, I_p the group of allp-adic integers. The torsion part of an Abelian groupG is throughout denoted bytG.Translated from Itogi Nauki i Tekhniki. Seriya Algebra, Topologiya, Geometriya, Vol. 23, pp. 51–118.