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{ring operator}β = β{ring operator}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. © 1991.