2004/02/24 by Eddy Godelle, Godelle, Eddy
Mathematics · #20F36 #FOS: Mathematics #Group Theory (math.GR) #math.GR #msc:20F36
paper · pdf · doi:10.48550/arxiv.math/0402389
arxiv created 2004/02/24 · arxiv updated 2009/12/01
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.