Uncountably many 22-generated just-infinite branch pro-22 groups

The aim of this note is to prove that there are $2^{\aleph_0}$ non-isomoprhic 2-generated just-infinite branch pro-$2$ groups

Universal groups of intermediate growth and their invariant random subgroups

We exhibit examples of groups of intermediate growth with ergodic continuous invariant random subgroups. The examples are the universal groups associated with a family of groups of intermediate growth

Profinite completion of Grigorchuk's group is not finitely presented

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

Orta büyümeli grupların Schreier çizgelerinin spektrumları

Bu projede orta büyümeli grupların Schreier çizgelerinin spektrumları hakkında araştırma yapılacaktır. Grubun yapısı ile spektrum arasındaki bağlantı incelenecektir

On the condensation property of the lamplighter groups and groups of intermediate growth

The aim of this short note is to revisit some old results about groups of intermediate growth and groups of the lamplighter type and to show that the Lamplighter group L = Z2 ≀ Z is a condensation group and has a minimal presentation by generators and relators. The condensation property is achieved by showing that L belongs to a Cantor subset of the space M2 of marked 2-generated groups consisting mostly of groups of intermediate growth