## On the left-distributive quasigroups.(Russian)Zbl 0592.20066

Main result: A group G with generator set E is the left-associated group of a left-distributive quasigroup if and only if the following two conditions are satisfied: (i) if two of the elements a, b, c satisfy the equation $$ab=bc$$ and belong to E then the remaining one is uniquely determined and belongs to E too, (ii) if $$a^ n=c$$ is independent of $$a\in E$$ for some natural number n then $$c=1$$. - Further there are specified special cases (of medial, right-distributive, commutative and symmetric quasigroups and also of TS-quasigroups, respectively). As an interesting fact it results that any group G with generator set E satisfying (i) and (ii) has trivial centre.
Reviewer: V.Havel

### MSC:

 20N05 Loops, quasigroups 20F05 Generators, relations, and presentations of groups
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