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Locally finite distributive quasigroups and CH-quasigroups. (Russian) Zbl 0566.20053
By a CH-quasigroup we mean a symmetric quasigroup in which any subquasigroup generated by three elements is abelian. A symmetric quasigroup Q(\(\cdot)\) is abelian if \(Q(+)\) (where \(x+y=k\cdot xy\), k being a fixed element of Q) is an abelian group. It is proved that every locally finite distributive quasigroup and every locally finite CH- quasigroup is isomorphic to the direct product of p-quasigroups \(Q_ p\), where, for each prime number \(p\neq 3\), \(Q_ p\) is medial.
MSC:
20N05 Loops, quasigroups
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