Geodesic
On representations of permutations groups as isometry groups of $n$-semimetric spaces
Algebra and discrete mathematics, Tome 19 (2015) no. 1, pp. 58-66

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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, isometry group.
Mots-clés : permutation group 
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     author = {Oleg Gerdiy and Bogdana Oliynyk},
     title = {On representations of permutations groups as isometry groups of $n$-semimetric spaces},
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     pages = {58--66},
     publisher = {mathdoc},
     volume = {19},
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     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a7/}
}
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Oleg Gerdiy; Bogdana Oliynyk. On representations of permutations groups as isometry groups of $n$-semimetric spaces. Algebra and discrete mathematics, Tome 19 (2015) no. 1, pp. 58-66. http://geodesic.mathdoc.fr/item/ADM_2015_19_1_a7/