SUBGROUPS OF THE FREE SEMIGROUP ON A BIORDERED SET IN WHICH PRINCIPAL IDEALS ARE SINGLETONS
Brett McElwee · Communications in Algebra · 2002
Easdown has conjectured that the subgroups of the free semigroup on an arbitrary biordered set are free. In this note a weaker conjecture is verified. It is shown that the subgroups of the free semigroup on a biordered set in which principal ideals are singletons are free. In addition, an expression is given for the ranks of the maximal subgroups. This generalizes a result due to Pastijn which involves the free semigroup on a rectangular biset.