University of Isfahan International Journal of Group Theory 2251-7650 15 2 2025 06 24 On Artin groups admitting retractions to parabolic subgroups 71 92 29556 10.22108/ijgt.2025.143611.1935 EN Bruno Aarón Cisneros De La Cruz SECIHITI - Unidad Oaxaca del Instituto de Matemáticas de la UNAM, Oaxaca, Mexico María Cumplido Instituto de Matemáticas de la Universidad de Sevilla (IMUS) and Departamento de Algebra, Facultad de Matemáticas, Universidad de Sevilla, Seville, Spain Islam Foniqi School of Engineering, Mathematics and Physics, University of East Anglia, Norwich, United Kingdom Journal Article 2024 12 07 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. Artin groups FC type parabolic subgroup retraction https://ijgt.ui.ac.ir/article_29556_76b25b53e8d5ec029e54b0559f3138ac.pdf