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ЖУРНАЛЫ // Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica // Архив

Bul. Acad. Ştiinţe Repub. Mold. Mat., 2007, номер 1, страницы 37–45 (Mi basm48)

Эта публикация цитируется в 1 статье

Power sets of $n$-ary quasigroups

G. Belyavskaya

Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova

Аннотация: 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.

Ключевые слова и фразы: Binary quasigroup, $k$-invertible $n$-ary operation, $n$-ary quasigroup, latin square, $n$-dimensional hypercube, latin power set, quasigroup power set, pairwise orthogonal set of $n$-ary quasigroups.

MSC: 20N05, 20N15, 05B07

Поступила в редакцию: 11.11.2006

Язык публикации: английский



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