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Type radicals and quasi-decompositions of torsion-free abelian groups

Part of: Abelian groups

Published online by Cambridge University Press:  09 April 2009

Oteo Mutzbauer
Oteo Mutzbauer
Affiliation:
Universität WürzburgMathematisches InstitutAm Hubland 8700 Würzburg Bundesrepublik Deutschland
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Abstract

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A composition sequence for a torsion-free abelian group A is an increasing sequenceof 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 homogeneous. If A has finite rank and all permutations ofone of its type sequences can be realized, then A is quasi-isomorphic to a direct sum of uniform groups.

MSC classification

Secondary: 20K15: Torsion-free groups, finite rank 20K20: Torsion-free groups, infinite rank
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 52 , Issue 2 , April 1992 , pp. 219 - 236
Copyright
Copyright © Australian Mathematical Society 1992

References

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