The Tits Alternative for Cat(0) Cubical Complexes

A Tits alternative theorem is proved in this paper for groups acting on CAT(0) cubical complexes. That is, a proof is given to show that if G is assumed to be a group for which there is a bound on the orders of its finite subgroups, and if G acts properly on a finite-dimensional CAT(0) cubical complex, then either G contains a free subgroup of rank 2, or G is finitely generated and virtually abelian. In particular, the above conclusion holds for any group G with a free action on a finite-dimensional CAT(0) cubical complex. 2000 Mathematics Subject Classification 20F67, 20E08.