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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
##### Keywords:
quasigroup; balanced identity
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