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A theorem on balanced identities. (Russian) Zbl 0544.20060
An identity \(w_ 1=w_ 2\) in a quasigroup \(Q(\cdot)\) is called balanced, if every free variable occurs in \(w_ 1\) and \(w_ 2\) exactly once. The main result is the following. Let a quasigroup \(Q(\cdot)\) satisfy a balanced identity \(w_ 1=w_ 2\). If \(w_ 1\) contains a subword xy, where x, y are free elements of \(Q(\cdot)\), and \(w_ 2\) contains no such subword, then \(Q(\cdot)\) is isotopic to a group.
Reviewer: L.M.Gluskin
MSC:
20N05 Loops, quasigroups
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