Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups

Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups

Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are nontrivial direct products. We deal with a special case of semidirect...

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Date:2017
Main Author: Daugulis, Peteris
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2017
Subjects:
semidirect product
direct product
diagonal action
generalized dihedral group
20E22
20D40
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/215
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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-215
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-2152017-07-02T21:58:40Z Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups Daugulis, Peteris semidirect product, direct product, diagonal action, generalized dihedral group 20E22, 20D40 Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are nontrivial direct products. We deal with a special case of semidirect product when the twisting homomorphism acts diagonally on a direct product, as well as with the case when the extending group is a direct product. We give applications of these results in the case of generalized dihedral groups and classic dihedral groups \(D_{2n}\). For \(D_{2n}\) we give a complete description of semidirect decompositions and values of minimal permutation degrees. Lugansk National Taras Shevchenko University 2017-07-03 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/215 Algebra and Discrete Mathematics; Vol 23, No 2 (2017) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/215/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/215/82 https://admjournal.luguniv.edu.ua/index.php/adm/article/downloadSuppFile/215/213 Copyright (c) 2017 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2017-07-02T21:58:40Z
collection OJS
language English
topic semidirect product
direct product
diagonal action
generalized dihedral group
20E22
20D40
spellingShingle semidirect product
direct product
diagonal action
generalized dihedral group
20E22
20D40
Daugulis, Peteris
Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups
topic_facet semidirect product
direct product
diagonal action
generalized dihedral group
20E22
20D40
format Article
author Daugulis, Peteris
author_facet Daugulis, Peteris
author_sort Daugulis, Peteris
title Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups
title_short Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups
title_full Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups
title_fullStr Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups
title_full_unstemmed Nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups
title_sort nonuniqueness of semidirect decompositions for semidirect products with directly decomposable factors and applications for dihedral groups
description Nonuniqueness of semidirect decompositions of groups is an insufficiently studied question in contrast to direct decompositions. We obtain some results about semidirect decompositions for semidirect products with factors which are nontrivial direct products. We deal with a special case of semidirect product when the twisting homomorphism acts diagonally on a direct product, as well as with the case when the extending group is a direct product. We give applications of these results in the case of generalized dihedral groups and classic dihedral groups \(D_{2n}\). For \(D_{2n}\) we give a complete description of semidirect decompositions and values of minimal permutation degrees.
publisher Lugansk National Taras Shevchenko University
publishDate 2017
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/215
work_keys_str_mv AT daugulispeteris nonuniquenessofsemidirectdecompositionsforsemidirectproductswithdirectlydecomposablefactorsandapplicationsfordihedralgroups
first_indexed 2025-07-17T10:33:35Z
last_indexed 2025-07-17T10:33:35Z
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