Geodesic
On Commutativity and Mediality of Polyagroup Cross Isomorphs
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 141-152.

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The notion of isotopy (cross isomorphism) of n-ary operations can be got from the well-known notion of isotopy (isomorphism) by replacing one of its components with a k-ary m-invertible operation [1, 2]. The idea of consideration of cross isotopy belongs to V. D. Belousov [3], who defined it for binary quasigroups. In the paper necessary and sufficient conditions for commutativity and mediality of a polyagroup cross isomorph (when n>2k) are determined. A neutrality criterion of an arbitrary element is stated. 
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F. M. Sokhatsky; O. V. Yurevych. On Commutativity and Mediality of Polyagroup Cross Isomorphs. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2005), pp. 141-152. https://geodesic-test.mathdoc.fr/item/BASM_2005_3_a11/

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[2] Yurevych O. V., “On cross isotopy of polyagrups”, Trudy instytuta prykladnoyi matematyky i mekhaniky NAN Ukrainy, 2005, no. 11, 34–49 (in Ukrainian) | MR

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