Antolín Pichel, YagoCumplido, María2023-06-172023-06-1720211472-274710.2140/agt.2021.21.1791https://hdl.handle.net/20.500.14352/8624Let A ≠ A1;A2;I2m be an irreducible Artin–Tits group of spherical type. We show that the periodic elements of A and the elements preserving some parabolic subgroup of A act elliptically on the additional length graph CAL(A), a hyperbolic, infinite diameter graph associated to A constructed by Calvez and Wiest to show that A/Z(A) is acylindrically hyperbolic. We use these results to find an element g ∈ A such that <P,g> ≅ P * <g> for every proper standard parabolic subgroup P of A. The length of g is uniformly bounded with respect to the Garside generators, independently of A. This allows us to show that, in contrast with the Artin generators case, the sequence ω(An,S)(with n ∈ N) of exponential growth rates of braid groups, with respect to the Garside generating set, goes to infinity.engjournal articlehttps://doi.org/10.2140/agt.2021.21.1791https://msp.org/agt/2021/21-4/p06.xhtmlopen access512.54Braid groupsArtin groupsGeometric group theoryÁlgebraGrupos (Matemáticas)1201 Álgebra