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.

DOI: 10.14232/actasm-013-271-3

AMS Subject Classification (1991): 08A35, 08C15, 20B27; 06Bxx, 20Mxx, 20N05

Keyword(s): idempotent algebra, transitive automorphism group, symmetry, quasivariety

Received March 25, 2013, and in revised form November 14, 2013. (Registered under 21/2013.)