On Artin groups admitting retractions to parabolic subgroups

Articles in Press

Document Type : Research Paper

Authors

1 SECIHITI - Unidad Oaxaca del Instituto de Matemáticas de la UNAM, Oaxaca, Mexico

2 Instituto de Matemáticas de la Universidad de Sevilla (IMUS) and Departamento de Algebra, Facultad de Matemáticas, Universidad de Sevilla, Seville, Spain

3 School of Engineering, Mathematics and Physics, University of East Anglia, Norwich, United Kingdom

10.22108/ijgt.2025.143611.1935

Abstract

We generalise the retractions to standard parabolic subgroups for even Artin groups to FC-type Artin groups and other more general families. We prove that these retractions uniquely extend to any parabolic subgroup. We use retractions to generalise the results of Antolín and Foniqi that reduce the problem of intersection of parabolic subgroups to weaker conditions. As a corollary, we characterise coherence for the FC case.

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References

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International Journal of Group Theory

Articles in Press, Corrected Proof
Available Online from 24 June 2025

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History

  • Receive Date: 07 December 2024
  • Revise Date: 21 May 2025
  • Accept Date: 29 May 2025
  • Published Online: 24 June 2025

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