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Parabolic subgroups inside parabolic subgroups of Artin groups.
- Source :
-
Proceedings of the American Mathematical Society . Apr2023, Vol. 151 Issue 4, p1519-1526. 8p. - Publication Year :
- 2023
-
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]. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ARTIN algebras
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00029939
- Volume :
- 151
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Proceedings of the American Mathematical Society
- Publication Type :
- Academic Journal
- Accession number :
- 161956713
- Full Text :
- https://doi.org/10.1090/proc/16289