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The weight of a Butler group. (Das Gewicht einer Butlergruppe.) (German) Zbl 0796.20042

There are several type invariants of torsion-free abelian groups of finite rank, the inner, outer, sum, Richman and hypertypes. The sum type of a torsion-free abelian group of finite rank for instance is the sum of types of the quotients of a chain of pure subgroups with ranks increasing by 1. The weight of a torsion-free abelian group of finite rank is defined as the map which maps a pure subgroup to its sum type. This type invariant “weight” covers all known type invariants. Goeters, Vinsonhaler, and Wickless proved in 1989 that the Richman type can be derived from the weight. In so far the weight can be considered the most precise invariant of torsion-free abelian groups of finite rank, given in terms of types.
Here the calculation with types has been developed considerably and is applied to Butler groups, i.e. torsion-free homomorphic images of completely decomposable groups of finite rank, a predestined group class in this context. The main result is a characterization of Butler groups (and of almost completely decomposable groups) by type conditions only.

MSC:

20K15 Torsion-free groups, finite rank
20K25 Direct sums, direct products, etc. for abelian groups
20K27 Subgroups of abelian groups
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References:

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