J Austral Math Soc Ser A 52 pp219--236, 1992.

Type Radicals and Quasi-Decompositions of Torsion-Free Abelian Groups

Otto Mutzbauer

Abstract

A composition sequence for a torsion-free abelian group A is an increasing sequence of pure subgroups with rank 1 quotients and union A. Properties of A can be described by the sequence of types of these quotients. For example, if A is uniform, that is all the types in some sequence are equal, then A is complete decomposable if it is homogenous. If A has finite rank and all permutations of one of its type sequences can be realized, then A is quasi-isomorphic to a direct sum of uniform groups.

1991 AMS Subject Classification: 20K15, 20K20

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Authors

Otto Mutzbauer

Universität Würzburg, Mathematisches Institut, Am Hubland, 8700 Würzburg, Bundesrepublik Deutschland.