Abelian subgroup structure of square complex groups and arithmetic of   quaternions
  A square complex is a 2-complex formed by gluing squares together. This article is concerned with the fundamental group $\Gamma$ of certain square complexes of nonpositive curvature, related to quaternion algebras. The abelian subgroup structure of $\Gamma$ is studied in some detail. 
Diego Rattaggi, Guyan Robertson