Idempotent Algebras and Symmetry
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Acta Scientiarum Mathematicarum
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The quasivariety consisting of all the algebras of a given type that can be embedded as a subalgebra into some algebra which has a transitive automorphism group contains the variety of all idempotent algebras of the given type: every idempotent algebra B can be embedded as a retract into an algebra which has a transitive automorphism group and which is simultaneously a subdirect power of B and a direct limit of powers of B. This result applies in particular to lattices, bands, Steiner quasigroups and so on.
Pastijn, Francis, "Idempotent Algebras and Symmetry" (2014). Mathematics, Statistics and Computer Science Faculty Research and Publications. 276.