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Algebra Discrete Math., 2015, Volume 19, Issue 1, Pages 58–66 (Mi adm507)  

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.

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Bibliographic databases:
MSC: 54B25, 20B25, 54E40
Received: 18.03.2015
Revised: 18.03.2015
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Citation: Oleg Gerdiy, Bogdana Oliynyk, “On representations of permutations groups as isometry groups of $n$-semimetric spaces”, Algebra Discrete Math., 19:1 (2015), 58–66

Citation in format AMSBIB
\Bibitem{GerOli15}
\by Oleg~Gerdiy, Bogdana~Oliynyk
\paper On representations of permutations groups as isometry groups of $n$-semimetric spaces
\jour Algebra Discrete Math.
\yr 2015
\vol 19
\issue 1
\pages 58--66
\mathnet{http://mi.mathnet.ru/adm507}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3376340}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000209846200007}


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