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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| Datum: | 2018 |
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| Format: | Artikel |
| Sprache: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1176 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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oai:ojs.admjournal.luguniv.edu.ua: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 |
| institution |
Algebra and Discrete Mathematics |
| baseUrl_str |
|
| datestamp_date |
2018-05-17T07:50:53Z |
| collection |
OJS |
| language |
English |
| topic |
\(n\)-semimetric permutation group isometry group 54B25 20B25 54E40 |
| 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 |
| topic_facet |
\(n\)-semimetric permutation group isometry group 54B25 20B25 54E40 |
| format |
Article |
| author |
Gerdiy, Oleg Oliynyk, Bogdana |
| author_facet |
Gerdiy, Oleg Oliynyk, Bogdana |
| author_sort |
Gerdiy, Oleg |
| title |
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_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_sort |
on representations of permutations groups as isometry groups of \(n\)-semimetric spaces |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1176 |
| work_keys_str_mv |
AT gerdiyoleg onrepresentationsofpermutationsgroupsasisometrygroupsofnsemimetricspaces AT oliynykbogdana onrepresentationsofpermutationsgroupsasisometrygroupsofnsemimetricspaces |
| first_indexed |
2025-07-17T10:32:21Z |
| last_indexed |
2025-07-17T10:32:21Z |
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1837889845235548160 |