Algebra Seminar "Residually finite groups as subgroups of branch groups", by Steffen Kionke (FernUni Hagen)
Title: Residually finite groups as subgroups of branch groups
Abstract: A group is a branch group, if it admits a "nice" action on a rooted tree. The class of branch groups contains a number of famous groups (e.g. the first Grigorchuk group) which are known for their exotic properties. We give a short introduction to branch groups and discuss some famous examples. We will see that branch groups are residually finite, this means, they admit many finite quotients. Then we explain a new method that allows to embed any residually finite group into a branch group. It turns out that this embedding preserves a number of properties. As an application, we obtain the first examples of non-amenable torsion branch groups.
This talk is based on joint work with Eduard Schesler.
Tid: 2023-09-27 15:15 till 16:15
anitha [dot] thillaisundaram [at] math [dot] lu [dot] se