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Crossed product of two systems of quasigroups and its use for the construction of partially orthogonal quasigroups. (Russian) Zbl 0583.20056

The main result of this paper is the following theorem: If there exists a system of \(s+1\) orthogonal quasigroups of order n and also an orthogonal set of a quasigroups of order m, then there exists an r-orthogonal system of quasigroups of order mn if \(r=km^ 2+(n-k)m+(n^ 2-n-t)p+(2m-p)tp\) for arbitrary k,p,t if \(0\leq k\leq n\), \(0\leq p\leq m\), \(0\leq t\leq k(n-1)\) hold.
Reviewer: J.Dénes

MSC:

20N05 Loops, quasigroups
05B15 Orthogonal arrays, Latin squares, Room squares
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