In geometric group theory we study various topological spaces and metric spaces on which a group G acts. The first of these is the group itself with the discrete topology. The next space of interest is the “Cayley graph.” It is a certain one dimensional cell complex with a G-action. Its definition depends on a choice of a set of generators S for G. Cayley graphs for G can be characterized as G-actions on connected graphs which are simply transitively on the vertex set (Theorem 2.1.1). Similarly, one can define a “Cayley 2-complex” for G to be any simply connected, two dimensional cell complex with a cellular G-action which is simply transitive on its vertex set.