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Article Dans Une Revue Proceedings of the American Mathematical Society Année : 2023

Parabolic subgroups inside parabolic subgroups of Artin groups

Résumé

We prove that a parabolic subgroup P P contained in another parabolic subgroup P ′ P’ of an Artin group A A is a parabolic subgroup of P ′ P’ . This answers a question of Godelle which is not obvious despite appearances. In order to achieve our result we construct a set-retraction A → P A \to P of the inclusion map from a parabolic subgroup P P into A A . This retraction was implicitly constructed in a previous paper by Charney and the second author [Bull. Lond. Math. Soc. 46 (2014), pp. 1248–1255].

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Dates et versions

hal-04311217 , version 1 (28-11-2023)

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Martín Blufstein, Luis Paris. Parabolic subgroups inside parabolic subgroups of Artin groups. Proceedings of the American Mathematical Society, 2023, 151 (4), pp.1519-1526. ⟨10.1090/proc/16289⟩. ⟨hal-04311217⟩
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