PLATONIC TRIANGLES OF GROUPS

Non-positively curved triangles of finite groups are of cohomological dimension 2 over the rationals and have Property FA. We classify trian gles of finite groups which satisfy certain geometric conditions inclu ding the Gauss-Bonnet theorem. We investigate whether or not these gro ups are virtually torsionfree, contain a free abelian subgroup of rank 2, are residually finite or are linear.