A characterization of congruence permutable locally finite varieties

A variety V of universal algebras is said to be congruence permutable if for every algebra A of V and every pair of congruences α, β from A we have α∘β = β∘α. We show that if V is locally finite (i.e., every finitely generated member of V is finite) then congruence permutability is equivalent to a local property of the finite members of V, expressible in the language of tame congruence theory. This answers a question of R. McKenzie and D. Hobby.