Universal diagram groups with identical Poincaré series. (Q531926)
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scientific article; zbMATH DE number 5880971
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Universal diagram groups with identical Poincaré series. |
scientific article; zbMATH DE number 5880971 |
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Universal diagram groups with identical Poincaré series. (English)
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21 April 2011
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Summary: For a diagram group \(G\), the first derived quotient \(G_1/G_2\) is always free Abelian (as proved by M. Sapir and V. Guba). However the second derived quotient \(G_2/G_3\) may contain torsion. In fact, we show that for any finite or countably infinite direct product of cyclic groups \(A\), there is a diagram group with second derived quotient \(A\). We use that to construct families with the properties of the title.
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diagram groups
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derived quotients
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FP-infinity
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Poincaré series
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homology groups
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0.85657907
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0.8546958
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0.8529069
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0.85227275
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0.85189193
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0.85080403
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0.85075784
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