On the topological full group containing the Grigorchuk group

Yaroslav Vorobets

On the topological full group containing the Grigorchuk group

Group Theory 2020-07-15 v1

Authors: Yaroslav Vorobets

Abstract

We consider the topological full group of a substitution subshift induced by a substitution $a\to aca$ , $b\to d$ , $c\to b$ , $d\to c$ . This group is interesting since the Grigorchuk group naturally embeds into it. We show that the topological full group is finitely generated and give a simple generating set for it.

Keywords

topological groups wreath product of groups group theory

Cite

@article{arxiv.2007.06789,
  title  = {On the topological full group containing the Grigorchuk group},
  author = {Yaroslav Vorobets},
  journal= {arXiv preprint arXiv:2007.06789},
  year   = {2020}
}