Parabolic subgroups inside parabolic subgroups of Artin groups
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- by Martín A. Blufstein and Luis Paris
- Proc. Amer. Math. Soc. 151 (2023), 1519-1526
- DOI: https://doi.org/10.1090/proc/16289
- Published electronically: January 26, 2023
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Abstract:
We prove that a parabolic subgroup $P$ contained in another parabolic subgroup $P’$ of an Artin group $A$ is a parabolic subgroup of $P’$. This answers a question of Godelle which is not obvious despite appearances. In order to achieve our result we construct a set-retraction $A \to P$ of the inclusion map from a parabolic subgroup $P$ into $A$. This retraction was implicitly constructed in a previous paper by Charney and the second author [Bull. Lond. Math. Soc. 46 (2014), pp. 1248–1255].References
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Bibliographic Information
- Martín A. Blufstein
- Affiliation: Departamento de Matemática - IMAS, FCEyN, Universidad de Buenos Aires, Buenos Aires, Argentina
- Email: mblufstein@dm.uba.ar
- Luis Paris
- Affiliation: IMB, UMR 5584, CNRS, Université Bourgogne Franche-Comté, 21000 Dijon, France
- MR Author ID: 249743
- Email: lparis@u-bourgogne.fr
- Received by editor(s): April 13, 2022
- Received by editor(s) in revised form: August 23, 2022, and September 13, 2022
- Published electronically: January 26, 2023
- Additional Notes: The first author was supported by CONICET. The second author was supported by the French project “AlMaRe” (ANR-19-CE40-0001-01) of the ANR
- Communicated by: Genevieve S. Walsh
- © Copyright 2023 by the authors
- Journal: Proc. Amer. Math. Soc. 151 (2023), 1519-1526
- MSC (2020): Primary 20F36
- DOI: https://doi.org/10.1090/proc/16289
- MathSciNet review: 4550347