Automorphism groups of superextensions of finite monogenic semigroups

A family \(\mathcal L\) of subsets of a set \(X\) is called linked if \(A\cap B\ne\emptyset\) for any \(A,B\in\mathcal L\). A linked family \(\mathcal M\) of subsets of \(X\) is maximal linked if \(\mathcal M\) coincides with each linked family \(\mathcal L\) on \(X\) that contains \(\mathcal M\)....

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Date:	2019
Main Authors:	Banakh, Taras O., Gavrylkiv, Volodymyr M.
Format:	Article
Language:	English
Published:	Lugansk National Taras Shevchenko University 2019
Subjects:	monogenic semigroup maximal linked upfamily superextension automorphism group 20D45 20M15 20B25
Online Access:	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1225
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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-1225
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spelling	oai:ojs.admjournal.luguniv.edu.ua:article-12252019-07-14T19:54:06Z Automorphism groups of superextensions of finite monogenic semigroups Banakh, Taras O. Gavrylkiv, Volodymyr M. monogenic semigroup, maximal linked upfamily, superextension, automorphism group 20D45, 20M15, 20B25 A family \(\mathcal L\) of subsets of a set \(X\) is called linked if \(A\cap B\ne\emptyset\) for any \(A,B\in\mathcal L\). A linked family \(\mathcal M\) of subsets of \(X\) is maximal linked if \(\mathcal M\) coincides with each linked family \(\mathcal L\) on \(X\) that contains \(\mathcal M\). The superextension \(\lambda(X)\) of \(X\) consists of all maximal linked families on \(X\). Any associative binary operation \(* : X\times X \to X\) can be extended to an associative binary operation \(*: \lambda(X)\times\lambda(X)\to\lambda(X)\). In the paper we study automorphisms of the superextensions of finite monogenic semigroups and characteristic ideals in such semigroups. In particular, we describe the automorphism groups of the superextensions of finite monogenic semigroups of cardinality \(\leq 5\). Lugansk National Taras Shevchenko University 2019-07-14 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1225 Algebra and Discrete Mathematics; Vol 27, No 2 (2019) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1225/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/1225/397 Copyright (c) 2019 Algebra and Discrete Mathematics
institution	Algebra and Discrete Mathematics
baseUrl_str
datestamp_date	2019-07-14T19:54:06Z
collection	OJS
language	English
topic	monogenic semigroup maximal linked upfamily superextension automorphism group 20D45 20M15 20B25
spellingShingle	monogenic semigroup maximal linked upfamily superextension automorphism group 20D45 20M15 20B25 Banakh, Taras O. Gavrylkiv, Volodymyr M. Automorphism groups of superextensions of finite monogenic semigroups
topic_facet	monogenic semigroup maximal linked upfamily superextension automorphism group 20D45 20M15 20B25
format	Article
author	Banakh, Taras O. Gavrylkiv, Volodymyr M.
author_facet	Banakh, Taras O. Gavrylkiv, Volodymyr M.
author_sort	Banakh, Taras O.
title	Automorphism groups of superextensions of finite monogenic semigroups
title_short	Automorphism groups of superextensions of finite monogenic semigroups
title_full	Automorphism groups of superextensions of finite monogenic semigroups
title_fullStr	Automorphism groups of superextensions of finite monogenic semigroups
title_full_unstemmed	Automorphism groups of superextensions of finite monogenic semigroups
title_sort	automorphism groups of superextensions of finite monogenic semigroups
description	A family \(\mathcal L\) of subsets of a set \(X\) is called linked if \(A\cap B\ne\emptyset\) for any \(A,B\in\mathcal L\). A linked family \(\mathcal M\) of subsets of \(X\) is maximal linked if \(\mathcal M\) coincides with each linked family \(\mathcal L\) on \(X\) that contains \(\mathcal M\). The superextension \(\lambda(X)\) of \(X\) consists of all maximal linked families on \(X\). Any associative binary operation \(* : X\times X \to X\) can be extended to an associative binary operation \(*: \lambda(X)\times\lambda(X)\to\lambda(X)\). In the paper we study automorphisms of the superextensions of finite monogenic semigroups and characteristic ideals in such semigroups. In particular, we describe the automorphism groups of the superextensions of finite monogenic semigroups of cardinality \(\leq 5\).
publisher	Lugansk National Taras Shevchenko University
publishDate	2019
url	https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1225
work_keys_str_mv	AT banakhtaraso automorphismgroupsofsuperextensionsoffinitemonogenicsemigroups AT gavrylkivvolodymyrm automorphismgroupsofsuperextensionsoffinitemonogenicsemigroups
first_indexed	2025-07-17T10:36:08Z
last_indexed	2025-07-17T10:36:08Z
_version_	1837890082913124352

Automorphism groups of superextensions of finite monogenic semigroups

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