On semigroup presentations and Adian graphs. (Q2483416)

Let \(\mathcal P\) be a semigroup presentation of the form \(\langle a_1,\dots,a_n\mid w_1=a_1,\dots,w_n=a_n\rangle\). In this paper we consider the semigroup defined by \(\mathcal P\) and its Adian graphs. We show that if both Adian graphs of \(\mathcal P\) are connected and if one of the Adian graphs of \(\mathcal P\) is a cycle graph then \(\mathcal P\) defines a group.