## 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

### Keywords:

orthogonal quasigroups
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