Tame Garside monoids

Garside groups are a natural family generalizing Artin–Tits groups of spherical type. Most properties of the latter extend to arbitrary Garside groups. However some properties, in particular those involving conjugacy, require an additional technical criterion, called tameness, introduced by Charney et al. in [Geom. Dedicata 105 (1) (2004) 171–188]. In this paper, we establish an effective tameness criterion. This criterion turns out to apply to the Garside group that was the most natural candidate for nontameness.