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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| Дата: | 2017 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
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Lugansk National Taras Shevchenko University
2017
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/215 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543426982445056 |
|---|---|
| author | Daugulis, Peteris |
| author_facet | Daugulis, Peteris |
| author_sort | Daugulis, Peteris |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2017-07-02T21:58:40Z |
| 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. |
| first_indexed | 2025-12-02T15:42:30Z |
| format | Article |
| id | admjournalluguniveduua-article-215 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:42:30Z |
| publishDate | 2017 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-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 |
| 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 |
| title | 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_short | 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 |
| topic | semidirect product direct product diagonal action generalized dihedral group 20E22 20D40 |
| topic_facet | semidirect product direct product diagonal action generalized dihedral group 20E22 20D40 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/215 |
| work_keys_str_mv | AT daugulispeteris nonuniquenessofsemidirectdecompositionsforsemidirectproductswithdirectlydecomposablefactorsandapplicationsfordihedralgroups |