  If the congruences of a semigroup are commutative, we say that the semigroup
is permutable. In a previous paper, A. Nagy showed that every permutable
semigroup satisfying an arbitrary non-trivial permutation identity is medial or
an ideal extension of a rectangular band by a non-trivial commutative nil
semigroup. The author raised the following problem: Is every permutable
semigroup satisfying a non-trivial permutation identity medial? In present
paper we give a positive answer for this problem.
