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 group of so...
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| Опубліковано в: : | Algebra and Discrete Mathematics |
|---|---|
| Дата: | 2015 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2015
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/152787 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On representations of permutations groups as isometry groups of n-semimetric spaces / O. Gerdiy, B. Oliynyk // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 58-66. — Бібліогр.: 13 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862602843207237632 |
|---|---|
| author | Gerdiy, O. Oliynyk, B. |
| author_facet | Gerdiy, O. Oliynyk, B. |
| citation_txt | On representations of permutations groups as isometry groups of n-semimetric spaces / O. Gerdiy, B. Oliynyk // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 58-66. — Бібліогр.: 13 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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.
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| first_indexed | 2025-11-28T05:22:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152787 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-28T05:22:49Z |
| publishDate | 2015 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Gerdiy, O. Oliynyk, B. 2019-06-12T20:53:34Z 2019-06-12T20:53:34Z 2015 On representations of permutations groups as isometry groups of n-semimetric spaces / O. Gerdiy, B. Oliynyk // Algebra and Discrete Mathematics. — 2015. — Vol. 19, № 1. — С. 58-66. — Бібліогр.: 13 назв. — англ. 1726-3255 2010 MSC:54B25, 20B25, 54E40. https://nasplib.isofts.kiev.ua/handle/123456789/152787 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. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On representations of permutations groups as isometry groups of n-semimetric spaces Article published earlier |
| spellingShingle | On representations of permutations groups as isometry groups of n-semimetric spaces Gerdiy, O. Oliynyk, B. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152787 |
| work_keys_str_mv | AT gerdiyo onrepresentationsofpermutationsgroupsasisometrygroupsofnsemimetricspaces AT oliynykb onrepresentationsofpermutationsgroupsasisometrygroupsofnsemimetricspaces |