ACTA issues

## On a problem of A. Nagy concerning permutable semigroups satisfying a non-trivial permutation identity

Attila Deák

Acta Sci. Math. (Szeged) 72:3-4(2006), 537-541
5935/2009

 Abstract. We say that a semigroup $S$ is a permutable semigroup if, for every congruences $\alpha$ and $\beta$ of $S$, $\alpha\circ \beta = \beta\circ \alpha$. In [4], 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 the present paper we give a positive answer for this problem. AMS Subject Classification (1991): 20M10 Received January 13, 2006, and in revised form June 7, 2006. (Registered under 5935/2009.)