MULTIFRACTION REDUCTION III: THE CASE OF INTERVAL MONOIDS

Patrick Dehornoy (1) , Friedrich Wehrung (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

We investigate gcd-monoids, which are cancellative monoids in which any two elements admit a left and a right gcd, and the associated reduction of multifractions (arXiv:1606.08991 and 1606.08995), a general approach to the Word Problem for the enveloping group. Here we consider the particular case of interval monoids associated with finite posets. In this way, we construct gcd-monoids, in which reduction of multifractions has prescribed properties not yet known to be compatible: semi-convergence of reduction without convergence, semi-convergence up to some level but not beyond, non-embeddability into the enveloping group (a strong negation of semi-convergence).

Mots clés: poset; interval monoid; gcd-monoid; enveloping group; Word Problem; multifraction; reduction; embeddability; semi-convergence; circuit; zigzag

Domaines: Théorie des groupes [math.GR]

Patrick Dehornoy, Friedrich Wehrung. MULTIFRACTION REDUCTION III: THE CASE OF INTERVAL MONOIDS. 2016. ⟨hal-01338434v2⟩