×

zbMATH — the first resource for mathematics

Type invariants of torsion-free Abelian groups. (English) Zbl 0677.20042
Abelian group theory, Proc. 4th Conf., Perth/Aust. 1987, Contemp. Math. 87, 133-154 (1989).
[For the entire collection see Zbl 0666.00004.]
This paper concerns the lattices of types and cotypes of a torsion-free abelian group. The author surveys the properties of inner, outer, sum, intersection and Richman types known for finite rank groups, and where possible, extends them to infinite rank. He describes a useful set of prototypes of groups designed to illustrate all possible behaviours of type invariants, and presents several applications to quotient- divisible and Butler groups.
Reviewer: P.Schultz

MSC:
20K15 Torsion-free groups, finite rank
20K20 Torsion-free groups, infinite rank