On profinite groups of type \(\mathrm{FP}_\infty\). (Q266119)
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scientific article; zbMATH DE number 6567871
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On profinite groups of type \(\mathrm{FP}_\infty\). |
scientific article; zbMATH DE number 6567871 |
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On profinite groups of type \(\mathrm{FP}_\infty\). (English)
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13 April 2016
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This is a very impressive result that solves an old problem of Peter Kropholler in the torsion free case. A pro-\(p\) group \(G\) is of type \(FP_\infty\) if all cohomology groups \(H^n(G,\mathbb F_p)\) are finite. The main result states that a soluble torsion free pro-\(p\) group of type \(FP_\infty\) is polycyclic (as a pro-\(p\) group). In particular, \(G\) is of finite cohomological dimension. This is an imense contribution into soluble pro-\(p\) groups.
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soluble pro-\(p\) groups
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groups of type \(FP_\infty\)
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cohomology groups
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soluble profinite groups
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profinite groups of finite cohomological dimension
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