The flat closing problem for buildings
  Using the notion of a strongly regular hyperbolic automorphism of a locally finite Euclidean building, we prove that any (not necessarily discrete) closed, co-compact subgroup of the type-preserving automorphisms group of a locally finite general non-spherical building contains a compact-by-Z^d subgroup, where d is the dimension of a maximal flat. 
Corina Ciobotaru
math.GR