Abstract

Let X X be a universal cover of a finite connected graph, G = Aut ⁡ ( X ) G = \operatorname {Aut} (X) , and Γ \Gamma a group acting discretely and cocompactly on X X , i.e., a uniform lattice on X X . We give a necessary condition for an elliptic element of G G to belong to a uniform lattice or to the commensurability group. By using this condition, we construct some explicit examples.

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