$On autotopies and automorphisms of $n$-ary linear quasigroups$

On autotopies and automorphisms of $n$-ary linear quasigroups

In this article we study structure of autotopies, automorphisms, autotopy groups and automorphism groups of $n$-ary linear quasigroups. We find a connection between automorphism groups of some special kinds of $n$-ary quasigroups (idempotent quasigroups, loops) and some isotopes of these quasi...

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Бібліографічні деталі
Дата:	2018
Автори:	Marini, Alberto, Shcherbacov, Victor
Формат:	Стаття
Мова:	English
Опубліковано:	Lugansk National Taras Shevchenko University 2018
Теми:	quasigroup automorphism $n$-ary quasigroup medial quasigroup $n$-ary $T$-quasigroup isotopy autotopy 20N15 20N05
Онлайн доступ:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/991
Теги:	Додати тег Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:	Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics

id	oai:ojs.admjournal.luguniv.edu.ua:article-991
record_format	ojs
spelling	oai:ojs.admjournal.luguniv.edu.ua:article-9912018-05-15T05:12:44Z On autotopies and automorphisms of $n$-ary linear quasigroups Marini, Alberto Shcherbacov, Victor quasigroup, automorphism, $n$-ary quasigroup, medial quasigroup, $n$-ary $T$-quasigroup, isotopy, autotopy 20N15, 20N05 In this article we study structure of autotopies, automorphisms, autotopy groups and automorphism groups of $n$-ary linear quasigroups. We find a connection between automorphism groups of some special kinds of $n$-ary quasigroups (idempotent quasigroups, loops) and some isotopes of these quasigroups. In binary case we find more detailed connections between automorphism group of a loop and automorphism group of some its isotope. We prove that every finite medial $n$-ary quasigroup of order greater than 2 has a non-identity automorphism group. We apply obtained results to give some information on automorphism groups of $n$-ary quasigroups that correspond to the ISSN code, the EAN code and the UPC code. Lugansk National Taras Shevchenko University 2018-05-15 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/991 Algebra and Discrete Mathematics; Vol 3, No 2 (2004) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/991/520 Copyright (c) 2018 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
collection	OJS
language	English
topic	quasigroup automorphism $n$-ary quasigroup medial quasigroup $n$-ary $T$-quasigroup isotopy autotopy 20N15 20N05
spellingShingle	quasigroup automorphism $n$-ary quasigroup medial quasigroup $n$-ary $T$-quasigroup isotopy autotopy 20N15 20N05 Marini, Alberto Shcherbacov, Victor On autotopies and automorphisms of $n$-ary linear quasigroups
topic_facet	quasigroup automorphism $n$-ary quasigroup medial quasigroup $n$-ary $T$-quasigroup isotopy autotopy 20N15 20N05
format	Article
author	Marini, Alberto Shcherbacov, Victor
author_facet	Marini, Alberto Shcherbacov, Victor
author_sort	Marini, Alberto
title	On autotopies and automorphisms of $n$-ary linear quasigroups
title_short	On autotopies and automorphisms of $n$-ary linear quasigroups
title_full	On autotopies and automorphisms of $n$-ary linear quasigroups
title_fullStr	On autotopies and automorphisms of $n$-ary linear quasigroups
title_full_unstemmed	On autotopies and automorphisms of $n$-ary linear quasigroups
title_sort	on autotopies and automorphisms of $n$-ary linear quasigroups
description	In this article we study structure of autotopies, automorphisms, autotopy groups and automorphism groups of $n$-ary linear quasigroups. We find a connection between automorphism groups of some special kinds of $n$-ary quasigroups (idempotent quasigroups, loops) and some isotopes of these quasigroups. In binary case we find more detailed connections between automorphism group of a loop and automorphism group of some its isotope. We prove that every finite medial $n$-ary quasigroup of order greater than 2 has a non-identity automorphism group. We apply obtained results to give some information on automorphism groups of $n$-ary quasigroups that correspond to the ISSN code, the EAN code and the UPC code.
publisher	Lugansk National Taras Shevchenko University
publishDate	2018
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/991
work_keys_str_mv	AT marinialberto onautotopiesandautomorphismsofnarylinearquasigroups AT shcherbacovvictor onautotopiesandautomorphismsofnarylinearquasigroups
first_indexed	2024-04-12T06:25:57Z
last_indexed	2024-04-12T06:25:57Z
_version_	1796109214735663104

On autotopies and automorphisms of \(n\)-ary linear quasigroups

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