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, $n\ge 2$, $1\le k\leq n$, 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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     author = {G. Belyavskaya},
     title = {Power sets of $n$-ary quasigroups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {37--45},
     publisher = {mathdoc},
     number = {1},
     year = {2007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2007_1_a2/}
}
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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. http://geodesic.mathdoc.fr/item/BASM_2007_1_a2/