Uniform Mal'cev algebras with small congruence lattices

Abstract

A congruence of an algebra is called uniform if all the congruence classes are of the same size. An algebra is called uniform if each of its congruences is uniform. All algebras with a group reduct have this property. We prove that almost every finite uniform Mal'cev algebra with a congruence lattice of height at most two is polynomially equivalent to an expanded group. © 2014 The Author(s).