Decompositions of local rigid ACD groups (Q2717732)
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scientific article; zbMATH DE number 1605321
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Decompositions of local rigid ACD groups |
scientific article; zbMATH DE number 1605321 |
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Decompositions of local rigid ACD groups (English)
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17 June 2001
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torsion-free Abelian groups
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almost completely decomposable groups
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direct decompositions
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rigid groups
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representing matrices
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indecomposable decompositions
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presentations
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0.8939469
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0.8937459
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0.88369614
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0.8780892
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0.8777282
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0.8749134
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0.8718042
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A rigid \(p\)-local almost completely decomposable (ACD) group is an Abelian torsion-free extension of a finite direct sum of incomparable rank 1 groups by a finite Abelian \(p\)-group. Such groups play a crucial role in the normally intractable theory of torsion-free Abelian groups because they admit unique indecomposable direct decompositions and moreover can be recognised from their presentations.NEWLINENEWLINENEWLINEIn this paper, the authors describe with copious examples linear algebraic algorithms to determine the indecomposable decomposition of an arbitrary rigid \(p\)-local ACD group given by its standard presentation.
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