2001/11/27 by Patrick Dehornoy, Dehornoy, Patrick
Computer Science · Mathematics · #05C25 #20F36 #20M05 #68Q42 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:05C25 #msc:20F36 #msc:20M05 #msc:68Q42 #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.math/0111275
arxiv created 2001/11/27 · openalex publication_date 2001/11/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A combinatorial property of prositive group presentations, called completeness, is introduced, with an effective criterion for recognizing complete presentations, and an iterative method for completing an incomplete presentation. We show how to directly read several properties of the associated monoid and group from a complete presentation: cancellativity or existence of common multiples in the case of the monoid, or isoperimetric inequality in the case of the group. In particular, we obtain a new criterion for recognizing that a monoid embeds in a group of fractions. Typical presentations eligible for the current approach are the standard presentations of the Artin groups and the Heisenberg group.