ON QUASI UNIVERSAL COVERS FOR GROUPS ACTING ON TREES WITH INVERSIONS

In this paper we show that if G is a group acting on a tree X with inversions and if (T; Y ) is a fundamental domain for the action of G on X, then there exist a group ?G and a tree ?X induced by (T; Y ) such that ?G acts on ?X with inversions, G is isomorphic to ? G, and X is isomorphic to ?X. The pair (? G; ?X) is called the quasi universal cover of (G;X) induced by the (T; Y ).