Separating quasi-convex subgroups in 7-systolic groups

Letbe a group acting without inversions and simply transitively on the top- dimensional simplices of some simply-connected simplicial complex X with "simplicial neg- ative curvature". Then the quasi-convex subgroups ofare convex-cocompact. Furthermore, if the action ofon X satisfies some additional condition called "extra-tilability", the quasi- convex subgroups ofare separable, i.e. every such subgroup is the intersection of finite index subgroups. The latter result applies to a large class of "simplicially negatively curved" groups recently constructed by Januszkiewicz and the second author.