Geodesic
$m$-medial $n$-quasigroups
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 1, pp. 9-14.

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For $n\geq 4$, every $n$-medial $n$-quasigroup is medial. If $1\leq m$, then there exist $m$-medial $n$-quasigroups which are not $(m+1)$-medial.
Classification : 20N05, 20N15
Keywords: $n$-quasigroup; medial 
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     title = {$m$-medial $n$-quasigroups},
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Kepka, Tomáš. $m$-medial $n$-quasigroups. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 1, pp. 9-14. http://geodesic.mathdoc.fr/item/CMUC_1991__32_1_a1/