# '22

36th Summer Topology Conference

July 18-22, 2022

University of Vienna, Department of Mathematics
Oskar-Morgenstern-Platz 1, 1090 Vienna, AUSTRIA

### "Lamplighter groups and bireversible automata"

#### Francoeur, Dominik

Bireversible automata are combinatorial objects that can be used to describe groups with self-similar actions on rooted trees. Groups defined by bireversible automata are interesting from the point of view of group theory, since they have connections, among others, with $CAT(0)$ square complexes and commensurators of free groups in the automorphism groups of regular trees. However, currently, very few examples of such groups are known and finding more is the subject of active research. In this talk, after reviewing the necessary notions, we will show that every group of the form $A\wr \mathbb{Z}$ with $A$ finite and abelian can be generated by a bireversible automaton, thus generalising a result of Skipper and Steinberg.

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