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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)

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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