Parabolic subgroups inside parabolic subgroups of Artin groups
| Autor: | Blufstein, Martin Axel, Paris, Luis |
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| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 8 pages. Accepted for publication in Proc. Amer. Math. Soc |
| Databáze: | arXiv |
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