Geodesic
On Rusakov’s $n$-ary $rs$-groups
Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 275-283
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Properties of $n$-ary groups connected with the affine geometry are considered. Some conditions for an $n$-ary $rs$-group to be derived from a binary group are given. Necessary and sufficient conditions for an $n$-ary group $\theta ,b>$-derived from an additive group of a field to be an $rs$-group are obtained. The existence of non-commutative $n$-ary $rs$-groups which are not derived from any group of arity $m2$ is proved.
Properties of $n$-ary groups connected with the affine geometry are considered. Some conditions for an $n$-ary $rs$-group to be derived from a binary group are given. Necessary and sufficient conditions for an $n$-ary group $\theta ,b>$-derived from an additive group of a field to be an $rs$-group are obtained. The existence of non-commutative $n$-ary $rs$-groups which are not derived from any group of arity $m$ for every $n\ge 3$, $r>2$ is proved.
Classification : 20N15, 51A25, 51D15
Keywords: $n$-ary group; symmetry 
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Dudek, Wiesław A.; Stojaković, Zoran. On Rusakov’s $n$-ary $rs$-groups. Czechoslovak Mathematical Journal, Tome 51 (2001) no. 2, pp. 275-283. http://geodesic.mathdoc.fr/item/CMJ_2001_51_2_a4/

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