The geometry of purely loxodromic subgroups of right-angled Artin groups

purely loxodromic subgroups of a right-angled Artin group A(\Gamma ) fulfill equivalent conditions that parallel characterizations of convex cocompactness in mapping class groups \mathrm {Mod}(S). In particular, such subgroups are quasiconvex in A(\Gamma ). In addition, we identify a milder condition for a finitely generated subgroup of A(\Gamma ) that guarantees it is free, undistorted, and retains finite generation when intersected with A(\Lambda ) for subgraphs \Lambda of \Gamma . These results have applications to both the study of convex cocompactness in \mathrm {Mod}(S) and the way in which certain groups can embed in right-angled Artin groups.]]>