1. Splitting Mixed Groups of Finite Torsion-Free Rank.
- Author
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Okuyama, Takashi
- Subjects
- *
ABELIAN groups , *GROUP theory , *MATHEMATICAL decomposition , *SET theory , *ALGEBRA , *PROOF theory - Abstract
First, we give a necessary and sufficient condition for torsion-free finite rank subgroups of arbitrary abelian groups to be purifiable. An abelian group G is said to be a strongly ADE decomposable group if there exists a purifiable T(G)-high subgroup of G. We use a previous result to characterize ADE decomposable groups of finite torsion-free rank. Finally, in an extreme case of strongly ADE decomposable groups, we give a necessary and sufficient condition for abelian groups of finite torsion-free rank to be splitting. [ABSTRACT FROM AUTHOR]
- Published
- 2004
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