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Type radicals and quasi-decompositions of torsion-free abelian groups
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Copyright © Australian Mathematical Society 1992
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