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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| Published in: | Algebra and Discrete Mathematics |
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| Date: | 2015 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут прикладної математики і механіки НАН України
2015
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/152787 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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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 |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
On representations of permutations groups as isometry groups of n-semimetric spaces |
| spellingShingle |
On representations of permutations groups as isometry groups of n-semimetric spaces Gerdiy, O. Oliynyk, B. |
| 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 |
| author |
Gerdiy, O. Oliynyk, B. |
| author_facet |
Gerdiy, O. Oliynyk, B. |
| publishDate |
2015 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/152787 |
| 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. |
| work_keys_str_mv |
AT gerdiyo onrepresentationsofpermutationsgroupsasisometrygroupsofnsemimetricspaces AT oliynykb onrepresentationsofpermutationsgroupsasisometrygroupsofnsemimetricspaces |
| first_indexed |
2025-11-28T05:22:49Z |
| last_indexed |
2025-11-28T05:22:49Z |
| _version_ |
1850853404745662464 |