Abstract
A quasigroup (Q,) satisfying the identityx(yx) =y (or the equivalent identity (xy)x =y) is called semisymmetric. Ann-quasigroup (Q, A) satisfying the identityA(A(x 1, ...,x n ),x 1, ...,x n−1) =x n is called cyclic. So, cyclicn-quasigroups are a generalization of semisymmetric quasigroups. In this paper, self-orthogonal cyclicn-quasigroups (SOCnQs) are considered. Some constructions ofSOCnQs are described and the spectrum of suchn-quasigroups investigated.
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Stojaković, Z., Paunić, D. Self-orthogonal cyclicn-quasigroups. Aeq. Math. 30, 252–257 (1986). https://doi.org/10.1007/BF02189931
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DOI: https://doi.org/10.1007/BF02189931