A characterization of congruence permutable locally finite varieties

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