THE CONJUGACY PROBLEM IN SMALL GAUSSIAN GROUPS

Abstract

Small Gaussian groups are a natural generalization of spherical Artin groups, namely groups of fractions of monoids in which the existence of least common multiples is kept as an hypothesis, but the relations between the generators are not supposed to necessarily be of Coxeter type. We show here how to extend the Elrifai–Morton solution for the conjugacy problem in braid groups to every small Gaussian group.

Keywords:

• Conjugacy
• Word problem
• Artin groups
• 2000 Mathematics Subject Classification: 20F05; 20F36; 20F10

ACKNOWLEDGMENTS

The author thanks Patrick Dehornoy for his help during the preparation of this work, and Paul–André Melliès for having introduced him to the Knuth–Bendix algorithm.