Parabolic subgroups of Garside groups
Group Theory
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/0402389,
title = {Parabolic subgroups of Garside groups},
author = {Eddy Godelle},
journal= {arXiv preprint arXiv:math/0402389},
year = {2007}
}