Parabolic subgroups of Garside groups
نویسنده
چکیده
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 LCMhomomorphisms between Artin-Tits groups. We prove that most of the properties of parabolic subgroups extend to this subgroups. 2000 Mathematics Subject Classification: 20F36, 03G10. keywords : Garside groups – lattices – parabolic subgroups.
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