2001.04743Jan 14, 202014 pages, a paper for Language and Automata Theory and Applications 2020 (extended version)

Nonstandard Cayley automatic representations of fundamental groups

Dmitry Berdinsky, Prohrak Kruengthomya

Group Theory Formal Languages and Automata Theory

Abstract

We construct a new family of Cayley automatic representations of semidirect products $\mathbb{Z}^n \rtimes_A \mathbb{Z}$ for which none of the projections of the normal subgroup $\mathbb{Z}^n$ onto each of its cyclic components is finite automaton recognizable. For $n=2$

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