Profinite completion of Grigorchuk's group is not finitely presented. (Q2909491)
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scientific article; zbMATH DE number 6074270
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Profinite completion of Grigorchuk's group is not finitely presented. |
scientific article; zbMATH DE number 6074270 |
Statements
30 August 2012
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groups acting on trees
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Grigorchuk group
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profinite completions
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Schur multipliers
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Profinite completion of Grigorchuk's group is not finitely presented. (English)
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\textit{R. I. Grigorchuk} has constructed a celebrated example of a finitely generated, infinite, periodic group [Funct. Anal. Appl. 14, 41-43 (1980); translation from Funkts. Anal. Prilozh. 14, No. 1, 53-54 (1980; Zbl 0595.20029)]. The goal of the paper under review is to show that the profinite completion of the Grigorchuk group is not finitely presented as a profinite group. This is accomplished by showing that its Schur multiplier over the field with two elements is infinite-dimensional.
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