On groups of reversible automata

A.S. Oliynyk

doi:10.15421/242528

On groups of reversible automata

A.S. Oliynyk (Taras Shevchenko National University of Kyiv), https://orcid.org/0000-0003-0940-7731

Abstract

For any nontrivial finite group $$$\mathbb{X}$$$ we construct a reversible automaton whose state set and alphabet coincide with $$$\mathbb{X}$$$, with transition and output functions defined by the left regular action of $$$\mathbb{X}$$$. We then study the associated automaton group $$$G_{\mathbb{X}}$$$ and prove, in particular, that $$$G_{\mathbb{X}}$$$ contains the lamplighter group $$$\mathbb{A} \wr \mathbb{Z}$$$, where $$$\mathbb{A}$$$ denotes the center of $$$\mathbb{X}$$$.

Keywords

reversible automaton; automaton group; lamplighter group

MSC 2020

Pri 20E08, Sec 20E22, 20E26

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