Pro-Hall \(R\)-groups and groups discriminated by the free pro-\(p\) group. (Q285582)
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scientific article; zbMATH DE number 6582602
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Pro-Hall \(R\)-groups and groups discriminated by the free pro-\(p\) group. |
scientific article; zbMATH DE number 6582602 |
Statements
Pro-Hall \(R\)-groups and groups discriminated by the free pro-\(p\) group. (English)
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19 May 2016
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fully residually free pro-\(p\) groups
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finitely generated pro-\(p\) groups
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limit groups
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extensions of centralisers
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free pro-Hall \(R\)-groups
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It is already a classical result that a fully residually free group is a finitely generated subgroup of a sequence of extensions of centralizers and vice versa. This is an open problem however for pro-\(p\) groups.NEWLINENEWLINE The paper gives a new approach to study the class of the fully residually free pro-\(p\) groups. The authors construct a new group \(F(X,R^{\mathrm{bin}})\) and prove that it contains some finitely generated pro-\(p\) groups that are fully residually free pro-\(p\).
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