  An algebraic structure is said to be congruence permutable if its arbitrary
congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta
=\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary
relations. For an arbitrary $G$-set $X$ with $G\cap X=\emptyset$, we define a
semigroup $(G,X,0)$ with a zero $0$ ($0\notin G\cup X$), and give necessary and
sufficient conditions for the congruence permutability of the $G$-set $X$ by
the help of the semigroup $(G,X,0)$.
