Nonstandard Cayley automatic representations of fundamental groups

Dmitry Berdinsky; Prohrak Kruengthomya

doi:10.1007/978-3-030-40608-0_7

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arXiv · 2001.04743

Nonstandard Cayley automatic representations of fundamental groups

Dmitry Berdinsky·Prohrak Kruengthomya

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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 $n=2$ we describe a family of matrices from $\mathrm{GL}(2,\mathbb{Z})$ corresponding to these representations. We are motivated by a problem of characterization of all possible Cayley automatic representations of these groups.

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Dmitry Berdinsky, Prohrak Kruengthomya. 2020-01-14. Nonstandard Cayley automatic representations of fundamental groups. https://doi.org/10.1007/978-3-030-40608-0_7

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