RESEARCH ARTICLE

On representations of permutations groups as isometry groups of $n$-semimetric spaces

Oleg Gerdiy, Bogdana Oliynyk

Department of Computer Sciences, National University of Kiev-Mohyla Academy

Abstract: 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.

Keywords: $n$-semimetric, permutation group, isometry group.

MSC: 54B25, 20B25, 54E40

Received: 18.03.2015
Revised: 18.03.2015

Language: English

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