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Article Dans Une Revue Journal of Algebra Année : 2020

Torsion subgroups of quasi-abelianized braid groups

Résumé

This article extends the works of Gonçalves, Guaschi, Ocampo [GGO] and Marin [MAR2] on finite subgroups of the quotients of generalized braid groups by the derived subgroup of their pure braid group. We get explicit criteria for subgroups of the (complex) reflection group to lift to subgroups of this quotient. In the specific case of the classical braid group, this enables us to describe all its finite subgroups : we show that every odd-order finite group can be embedded in it, when the number of strands goes to infinity. We also determine a complete list of the irreducible reflection groups for which this quotient is a Bieberbach group.
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Dates et versions

hal-01582323 , version 1 (05-09-2017)

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Paternité - Pas d'utilisation commerciale

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Vincent Beck, Ivan Marin. Torsion subgroups of quasi-abelianized braid groups. Journal of Algebra, 2020, ⟨10.1016/j.jalgebra.2019.07.009⟩. ⟨hal-01582323⟩
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