English

Profinite completion of Grigorchuk's group is not finitely presented

Group Theory 2012-06-13 v2

Abstract

In this paper we prove that the profinite completion G^\mathcal{\hat G} of the Grigorchuk group G\mathcal{G} is not finitely presented as a profinite group. We obtain this result by showing that H2(G^,\fieldF2)H^2(\mathcal{\hat G},\field{F}_2) is infinite dimensional. Also several results are proven about the finite quotients G/StG(n)\mathcal{G}/ St_{\mathcal{G}}(n) including minimal presentations and Schur Multipliers.

Keywords

Cite

@article{arxiv.1011.3880,
  title  = {Profinite completion of Grigorchuk's group is not finitely presented},
  author = {Mustafa Gokhan Benli},
  journal= {arXiv preprint arXiv:1011.3880},
  year   = {2012}
}