Parabolic subgroups of Garside groups

Eddy Godelle (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

A Garside monoid is a cancellative monoid with a finite lattice generating set; a Garside group is the group of fractions of a Garside monoid. The family of Garside groups contains the Artin-Tits groups of spherical type. We generalise the well-known notion of a parabolic subgroup of an Artin-Tits group into that of a parabolic subgroup of a Garside group. We also define the more general notion of a Garside subgroup of a Garside group, which is related to the notion of LCM-homomorphisms between Artin-Tits groups. We prove that most of the properties of parabolic subgroups extend to this subgroups.

Mots clés: Garside groups; lattice; parabolic subgroups

Domaines: Théorie des groupes [math.GR]

Eddy Godelle. Parabolic subgroups of Garside groups. 2004. ⟨hal-00001178⟩