Abstract:
In this article, we study the connections between orthogonality and retract
orthogonality of operations. We prove that if a tuple of operations is retractly orthogonal, then it is orthogonal. However, the orthogonality of operations doesn’t provide
their retract orthogonality. Consequently, every k-tuple of orthogonal k-ary operations is prolongable to a k-tuple of orthogonal n-ary operations. Also, we give some
specifications for central quasigroups. In particular for central quasigroups over finite
field of prime order, retract orthogonality is the necessary and sufficient condition for
orthogonality. The problem of coincidence of orthogonality and retract orthogonality
remains open.
