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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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/

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