On representations of permutations groups as isometry groups of \(n\)-semimetric spaces
We prove that every finite permutation group can be represented as the isometry group of some \(n\)-semimetric space. We show that if a finite permutation group can be realized as the isometry group of some \(n\)-semimetric space then this permutation group can be represented as the isometry gro...
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| Дата: | 2018 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Теми: | |
| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1176 |
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| Назва журналу: | Algebra and Discrete Mathematics |
Репозитарії
Algebra and Discrete Mathematics| _version_ | 1856543237327552512 |
|---|---|
| author | Gerdiy, Oleg Oliynyk, Bogdana |
| author_facet | Gerdiy, Oleg Oliynyk, Bogdana |
| author_sort | Gerdiy, Oleg |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-05-17T07:50:53Z |
| description | We prove that every finite permutation group can be represented as the isometry group of some \(n\)-semimetric space. We show that if a finite permutation group can be realized as the isometry group of some \(n\)-semimetric space then this permutation group can be represented as the isometry group of some \((n+1)\)-semimetric space. The notion of the semimetric rank of a permutation group is introduced. |
| first_indexed | 2025-12-02T15:29:47Z |
| format | Article |
| id | admjournalluguniveduua-article-1176 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:29:47Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-11762018-05-17T07:50:53Z On representations of permutations groups as isometry groups of \(n\)-semimetric spaces Gerdiy, Oleg Oliynyk, Bogdana \(n\)-semimetric, permutation group, isometry group 54B25, 20B25, 54E40 We prove that every finite permutation group can be represented as the isometry group of some \(n\)-semimetric space. We show that if a finite permutation group can be realized as the isometry group of some \(n\)-semimetric space then this permutation group can be represented as the isometry group of some \((n+1)\)-semimetric space. The notion of the semimetric rank of a permutation group is introduced. Lugansk National Taras Shevchenko University 2018-05-17 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1176 Algebra and Discrete Mathematics; Vol 19, No 1 (2015) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1176/665 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | \(n\)-semimetric permutation group isometry group 54B25 20B25 54E40 Gerdiy, Oleg Oliynyk, Bogdana On representations of permutations groups as isometry groups of \(n\)-semimetric spaces |
| title | On representations of permutations groups as isometry groups of \(n\)-semimetric spaces |
| title_full | On representations of permutations groups as isometry groups of \(n\)-semimetric spaces |
| title_fullStr | On representations of permutations groups as isometry groups of \(n\)-semimetric spaces |
| title_full_unstemmed | On representations of permutations groups as isometry groups of \(n\)-semimetric spaces |
| title_short | On representations of permutations groups as isometry groups of \(n\)-semimetric spaces |
| title_sort | on representations of permutations groups as isometry groups of \(n\)-semimetric spaces |
| topic | \(n\)-semimetric permutation group isometry group 54B25 20B25 54E40 |
| topic_facet | \(n\)-semimetric permutation group isometry group 54B25 20B25 54E40 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1176 |
| work_keys_str_mv | AT gerdiyoleg onrepresentationsofpermutationsgroupsasisometrygroupsofnsemimetricspaces AT oliynykbogdana onrepresentationsofpermutationsgroupsasisometrygroupsofnsemimetricspaces |