Monoids of O-type, subword reversing, and ordered groups

Patrick Dehornoy (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We describe a simple scheme for constructing finitely generated monoids in which left-divisibility is a linear ordering and for practically investigating these monoids. The approach is based on subword reversing, a general method of combinatorial group theory, and connected with Garside theory, here in a non-Noetherian context. As an application we describe several families of ordered groups whose space of left-invariant orderings has an isolated point, including torus knot groups and some of their amalgamated products.

Mots clés: monoid presentation; subword reversing; divisibility; quasi-central element; ordered group; space of orderings; Garside theory

Domaines: Théorie des groupes [math.GR]

Patrick Dehornoy. Monoids of O-type, subword reversing, and ordered groups. 2012. ⟨hal-00687691v3⟩