On a finite state representation of \(GL(n,\mathbb{Z})\)

It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups \(GL(n,\mathbb{Z})\).  The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of \(GL(2,\mathbb{Z})\) over an alphabet of size \(4\)  a...

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Date:2023
Main Authors: Oliynyk, A., Prokhorchuk, V.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2023
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Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-2158
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spelling oai:ojs.admjournal.luguniv.edu.ua:article-21582023-12-11T16:21:07Z On a finite state representation of \(GL(n,\mathbb{Z})\) Oliynyk, A. Prokhorchuk, V. automorphism of rooted tree, finite state automorphism, integer matrix, free group 20E08, 20E22, 20E26 It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups \(GL(n,\mathbb{Z})\).  The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of \(GL(2,\mathbb{Z})\) over an alphabet of size \(4\)  a finite state  representation of the free group of rank \(2\) over binary alphabet is constructed. Lugansk National Taras Shevchenko University 2023-12-11 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158 10.12958/adm2158 Algebra and Discrete Mathematics; Vol 36, No 1 (2023) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158/pdf_1 Copyright (c) 2023 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2023-12-11T16:21:07Z
collection OJS
language English
topic automorphism of rooted tree
finite state automorphism
integer matrix
free group
20E08
20E22
20E26
spellingShingle automorphism of rooted tree
finite state automorphism
integer matrix
free group
20E08
20E22
20E26
Oliynyk, A.
Prokhorchuk, V.
On a finite state representation of \(GL(n,\mathbb{Z})\)
topic_facet automorphism of rooted tree
finite state automorphism
integer matrix
free group
20E08
20E22
20E26
format Article
author Oliynyk, A.
Prokhorchuk, V.
author_facet Oliynyk, A.
Prokhorchuk, V.
author_sort Oliynyk, A.
title On a finite state representation of \(GL(n,\mathbb{Z})\)
title_short On a finite state representation of \(GL(n,\mathbb{Z})\)
title_full On a finite state representation of \(GL(n,\mathbb{Z})\)
title_fullStr On a finite state representation of \(GL(n,\mathbb{Z})\)
title_full_unstemmed On a finite state representation of \(GL(n,\mathbb{Z})\)
title_sort on a finite state representation of \(gl(n,\mathbb{z})\)
description It is examined finite state automorphisms of regular rooted trees constructed in [6] to represent groups \(GL(n,\mathbb{Z})\).  The number of states of automorphisms that correspond to elementary matrices is computed. Using the representation of \(GL(2,\mathbb{Z})\) over an alphabet of size \(4\)  a finite state  representation of the free group of rank \(2\) over binary alphabet is constructed.
publisher Lugansk National Taras Shevchenko University
publishDate 2023
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/2158
work_keys_str_mv AT oliynyka onafinitestaterepresentationofglnmathbbz
AT prokhorchukv onafinitestaterepresentationofglnmathbbz
first_indexed 2025-07-17T10:31:08Z
last_indexed 2025-07-17T10:31:08Z
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