On representations of permutations groups as isometry groups of \(n\)-semimetric spaces

• Date: 2018
• Main Authors: Gerdiy, Oleg, Oliynyk, Bogdana
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: \(n\)-semimetric; permutation group; isometry group; 54B25; 20B25; 54E40
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1176
• Journal Title: Algebra and Discrete Mathematics

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...