Abstract We show that the geometric realisation of poset proper parabolic subgroups a large-type Artin group has systolic geometry. use this geometry to set is stable under arbitrary intersections and forms lattice for inclusion. As an application, we groups are taking roots completely characterise conjugacy stable. also perspective recover unify results describing normalisers groups.

In this paper, we prove that all Euclidean Artin–Tits groups are acylindrically hyperbolic. To any Garside group of finite type, Wiest and the author associated a hyperbolic graph called additional length they used it to show central quotients spherical type general, is not priori but McCammond Sulway have shown embeds into an infinite-type which call crystallographic group. We associate exhibi...