On one-relator groups and units of special one-relation inverse monoids

This paper investigates and clarifies some connections between the theory of one-relator groups special one-relation inverse monoids, i.e. those monoids with a presentation form [Formula: see text]. We show that every group admits monoid presentation. subsequently consider classes text] which can be defined by presentations in defining word is arbitrary; reduced; cyclically or positive, respectively. inclusions are all strict. Conditional on natural conjecture, we prove Following this, use Benois algorithm recently devised Gray Ruškuc to produce an infinite family exhibit similar pathological behavior (which term O’Haresque) O’Hare respect computing minimal invertible pieces word. Finally, provide counterexample conjecture always correctly computes monoid.