### Prof. Dr. Rostislav Grigorchuk (Texas A&M University): Self-replicating, liftable and scale groups

##### Monday, 04.09.2023 13:30 im Raum SRZ 216/217

Abstract: Scale groups are closed subgroups of the group of isometries of the regular tree that fix an end of the tree and are vertex-transitive. They play an important role in the study of locally compact totally disconnected groups as was observed by G.Willis. It is a miracle that they are closely related to self-replicating groups, a special subclass of self-similar groups. In my talk I will discuss two ways of building scale groups. One is based on the use of scale-invariant groups studied by V.Nekrashevych and G.Pete, and a second is based on the use of liftable groups -- a special class of self-replicating groups. Examples based on both approaches will be demonstrated, including the Lamplighter group L and a torsion 2-group of intermediate growth G. It will be shown that G?, the finitely presented non elementary amenable relative of G, gives an example of a scale group acting 2-transitively on a punctured boundary. Additionally the group of isometries of the ring of integer p-adics and group of dilations of the field of p-adic numbers will be mentioned in the relation with the discussed topics. The talk is based on joint work with D.Savchuk which is inspired by the work of G.Willis "Scale groups".

Angelegt am 29.08.2023 von Carolin Gietz

Geändert am 29.08.2023 von Carolin Gietz

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