Congruence-permutable algebra

In the mathematical field of universal algebra, two congruences $\alpha ,\beta$ are said to be permutable if $\alpha \circ \beta =\beta \circ \alpha$. An algebra is congruence permutable if all of its congruences are permutable. A variety of algebras is congruence permutable if every algebra in the variety is congruence permutable.

A Mal'cev term is a term $M$ such that $M(x,x,y)=y=M(y,x,x).$

A variety is congruence permutable if and only if its signature contains a Mal'cev term.