English

Generalized Grigorchuk's Overgroups as points on $\mathcal{M}_k$

Group Theory 2019-11-06 v2

Abstract

Following the construction from `Degrees of growth of finitely generated groups and the theory of invariant means' we generalize the Grigorchuk's overgroup G~\tilde{\mathcal{G}}, studied in `On parabolic subgroups and Hecke algebras of some fractal groups' to the family {G~ω,ωΩ={0,1,2}N}\{ \tilde{G}_\omega, \omega \in \Omega = \{ 0, 1, 2 \}^\mathbb{N} \} of generalized Grigorchuk's overgroups. We consider these groups as 8-generated and describe the closure of this family in the space M8\mathcal{M}_8 of marked groups.

Keywords

Cite

@article{arxiv.1909.04575,
  title  = {Generalized Grigorchuk's Overgroups as points on $\mathcal{M}_k$},
  author = {Supun T. Samarakoon},
  journal= {arXiv preprint arXiv:1909.04575},
  year   = {2019}
}
R2 v1 2026-06-23T11:11:18.724Z