# Profinite completion of Grigorchuk&#x27;s group is not finitely presented - Mathematics > Group Theory

Abstract: In this paper we prove that the profinite completion $\mathcal{\hat G}$ ofthe Grigorchuk group $\mathcal{G}$ is not finitely presented as a profinitegroup. We obtain this result by showing that $H^2\mathcal{\hatG},\field{F} 2$ is infinite dimensional. Also several results are proven aboutthe finite quotients $\mathcal{G}- St {\mathcal{G}}n$ including minimalpresentations and Schur Multipliers.

Author: Mustafa Gokhan Benli

Source: https://arxiv.org/