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Have you forgotten your login? Volker Gebhardt 3 AuthorId: Bert Wiest 1 AuthorId: Fernando, 4, C. Hide details.

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We show that, in an Artin-Tits group of spherical type, the intersection of two parabolic subgroups is a parabolic subgroup. Moreover, we show that the tits of parabolic subgroups forms a lattice with respect to inclusion.

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This extends to all Artin-Tits groups of spherical type a result that was previously known for braid groups. To obtain the above results, we show that every element in an Artin-Tits group of spherical type admits a unique minimal parabolic subgroup containing it.

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Also, the subgroup associated to an element coincides with groups subgroup associated to any of its powers or indiancoligsex. As a consequence, if an element belongs to a parabolic subgroup, all its roots belong to the same parabolic subgroup. Document type: Journal articles. Monday, January 15, - 2: