Geodesic
Power sets of n-ary quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 37-45.

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In the theory of latin squares and in the binary quasigroup theory the notion of a latin power set (a quasigroup power set) is known. These sets have a good property, and namely, they are orthogonal sets. Such sets were studied and methods of their construction were suggested in different articles (see, for example, [1–5]). In this article we introduce (k)-powers of a k-invertible n-ary operation (with respect to the k-multiplication of n-ary operations) and (k)-power sets of n-ary quasigroups, n≥2, 1≤k≤n, prove pairwise orthogonality of such sets and consider distinct posibilities of their construction with the help of binary groups, in particular, using n – T-quasigroups and n-ary groups. 
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G. Belyavskaya. Power sets of $n$-ary quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 1 (2007), pp. 37-45. https://geodesic-test.mathdoc.fr/item/BASM_2007_1_a2/

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