Abstract. 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 \(\mathbf B\) can be embedded as a retract into an algebra which has a transitive automorphism group and which is simultaneously a subdirect power of \(\mathbf B\) and a direct limit of powers of \(\mathbf B\). This result applies in particular to lattices, bands, Steiner quasigroups and so on.
AMS Subject Classification
(1991): 08A35, 08C15, 20B27; 06Bxx, 20Mxx, 20N05
transitive automorphism group,
Received March 25, 2013, and in revised form November 14, 2013. (Registered under 21/2013.)