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Direct decompositions of quasi-groups. (Russian) Zbl 0635.20036
It is proved that the direct decompositions of a quasigroup Q into n factors are in a one-to-one correspondence with the n-tuples $$A_ 1,...,A_ n$$ of normal subsets of Q such that $$Q=A_ 1A_ 2...A_ n$$ (with respect to some arrangement of parentheses) and such that for every i, the intersection of $$A_ i$$ with $$A_ 1...A_{i-1}A_{i+1}...A_ n$$ consists of one element.
Reviewer: J.Ježek

##### MSC:
 20N05 Loops, quasigroups
##### Keywords:
direct decompositions; quasigroup; normal subsets
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