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arXiv · 1011.3880

Profinite completion of Grigorchuk's group is not finitely presented

Mustafa Gokhan Benli
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Abstract

In this paper we prove that the profinite completion $\mathcal{\hat G}$ of the Grigorchuk group $\mathcal{G}$ is not finitely presented as a profinite group. We obtain this result by showing that $H^2(\mathcal{\hat G},\field{F}_2)$ is infinite dimensional. Also several results are proven about the finite quotients $\mathcal{G}/ St_{\mathcal{G}}(n)$ including minimal presentations and Schur Multipliers.

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BibTeXRIS

Mustafa Gokhan Benli. 2012-02-02. Profinite completion of Grigorchuk's group is not finitely presented. https://doi.org/10.1142/s0218196712500452

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