Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle

We construct a new family of Cayley automatic representations of semidirect products [Formula: see text] for which none of the projections of the normal subgroup [Formula: see text] onto each of its cyclic components is finite automaton recognizable. For [Formula: see text] we describe a family of m...

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Autores principales: Berdinsky, Dmitry, Kruengthomya, Prohrak
Formato: Online Artículo Texto
Lenguaje:English
Publicado: 2020
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7206626/
http://dx.doi.org/10.1007/978-3-030-40608-0_7
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author Berdinsky, Dmitry
Kruengthomya, Prohrak
author_facet Berdinsky, Dmitry
Kruengthomya, Prohrak
author_sort Berdinsky, Dmitry
collection PubMed
description We construct a new family of Cayley automatic representations of semidirect products [Formula: see text] for which none of the projections of the normal subgroup [Formula: see text] onto each of its cyclic components is finite automaton recognizable. For [Formula: see text] we describe a family of matrices from [Formula: see text] 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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spelling pubmed-72066262020-05-08 Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle Berdinsky, Dmitry Kruengthomya, Prohrak Language and Automata Theory and Applications Article We construct a new family of Cayley automatic representations of semidirect products [Formula: see text] for which none of the projections of the normal subgroup [Formula: see text] onto each of its cyclic components is finite automaton recognizable. For [Formula: see text] we describe a family of matrices from [Formula: see text] corresponding to these representations. We are motivated by a problem of characterization of all possible Cayley automatic representations of these groups. 2020-01-07 /pmc/articles/PMC7206626/ http://dx.doi.org/10.1007/978-3-030-40608-0_7 Text en © Springer Nature Switzerland AG 2020 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Berdinsky, Dmitry
Kruengthomya, Prohrak
Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle
title Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle
title_full Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle
title_fullStr Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle
title_full_unstemmed Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle
title_short Nonstandard Cayley Automatic Representations for Fundamental Groups of Torus Bundles over the Circle
title_sort nonstandard cayley automatic representations for fundamental groups of torus bundles over the circle
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7206626/
http://dx.doi.org/10.1007/978-3-030-40608-0_7
work_keys_str_mv AT berdinskydmitry nonstandardcayleyautomaticrepresentationsforfundamentalgroupsoftorusbundlesoverthecircle
AT kruengthomyaprohrak nonstandardcayleyautomaticrepresentationsforfundamentalgroupsoftorusbundlesoverthecircle

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