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Group conjugation has non-trivial LD-identities. (English) Zbl 0810.20053
A groupoid $$\langle A,* \rangle$$ is said to be left cancellative if $$x * y = x * z$$ implies $$y = z$$ for any $$x, y,z \in A$$. Left distributive groupoids are defined by the identity $$x * (y * z) = (x * y) * (x * z)$$. Given a group $$\langle G,\cdot,^{-1}\rangle$$ the group conjugation $$*$$ on $$G$$ is introduced by the rule $$x * y = xyx^{-1}$$. It is shown that group conjugation generates a proper subvariety of left distributive idempotent groupoids. This subvariety coincides with the variety generated by all cancellative left distributive groupoids.
Reviewer: J.Duda (Brno)

##### MSC:
 20N02 Sets with a single binary operation (groupoids) 20A05 Axiomatics and elementary properties of groups 08B15 Lattices of varieties 20M07 Varieties and pseudovarieties of semigroups
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