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Abelian groups. (English) Zbl 0848.20046
This fifth survey of reviews on abelian groups comprises papers reviewed in 1985-1992. Just as in the preceding surveys, the issues concerning finite abelian groups, topological groups, ordered groups, group algebras, modules (with rare exceptions), and topics on logic are not considered. The issues on the lattice of subgroups of an abelian group are included in Section 11. In contrast to the fourth survey [the author, Itogi Nauki Tekh., Ser. Algebra, Topologiya, Geom. 23, 51-118 (1985; Zbl 0605.20052)], this one does not contain Sections 6 (\(N\)-high subgroups), 9 (rings with a given additive group), and 10 (valuated groups); since only a few papers treated these topics, the material discussed earlier in Sections 9, and 10 is now included in Section 11 and the material of the former Section 6 will be found in Sections 1, 7, 8, and 11 of this survey. On the other hand, the fifth survey has three new sections devoted to separable groups (a new Sect. 5), Butler groups (a new Sect. 6), and the endomorphism rings and automorphism groups of abelian groups (a new Sect. 9).

MSC:
20Kxx Abelian groups
20K10 Torsion groups, primary groups and generalized primary groups
20K21 Mixed groups
20K15 Torsion-free groups, finite rank
20K25 Direct sums, direct products, etc. for abelian groups
20K20 Torsion-free groups, infinite rank
20K30 Automorphisms, homomorphisms, endomorphisms, etc. for abelian groups
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