Bireversible automata generating lamplighter groups

TL;DR

This paper constructs bireversible automata that generate lamplighter groups, specifically for every non-trivial finite abelian group, expanding the understanding of automata groups and their algebraic properties.

Contribution

It introduces a method to produce bireversible automata for all lamplighter groups over non-trivial finite abelian groups, a novel general construction.

Findings

Automata generate lamplighter groups $A \,\wr\, \mathbb{Z}$

Applicable to all non-trivial finite abelian groups

Advances automata group theory

Abstract

For every non-trivial finite abelian group $A$, we exhibit a bireversible automaton generating the lamplighter group $A \wr \mathbb{Z}$.