The syntactic semigroup problem is to decide whether a given finite semigroup is syntactic or not. This work investigates the syntactic semigroup problem for both the semigroup reducts of A(Bn), the affine nearsemiring over a Brandt semigroup Bn. It is ascertained that both the semigroup reducts of A(Bn) are syntactic semigroups.

It is known that for any finite group G given by a finite group presentation 〈A |R 〉 there exists a finite semigroup presentation 〈 B | Q 〉 for G of the same deficiency, i.e. satisfying |Q| − |B| = |R| − |A|. It is also known that the analogous statement does not hold for all finite monoids. In this paper we give a necessary and sufficient condition for a finite monoid M , given by a finite mon...