Year: 2025
Type: article
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 $\mathbb{X}$.
Source: Researches in Mathematics
DOI: 10.15421/242528
Author: A.S. Oliynyk
Institution: Taras Shevchenko National University of Kyiv
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $20
OpenAlex ID: W7127330059
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