Congruence uniformity

An algebra is congruence uniform if for all congruence relations $\theta$ of the algebra it holds that all congruence classes of $\theta$ have the same cardinality.

A class of algebras is congruence uniform if each of its members is congruence uniform.

Congruence uniformity holds for many 'classical' varieties such as groups, rings and vector spaces.

This property can be characterized by a Mal'cev condition …