Abstract
Let X be a locally finite tree. Then G = Aut(X) is a locally compact group, where two automorphisms are close if they agree on a large finite subtree. For χεVX the stabilizer G x is open, and compact; in fact $$G_x = \lim_{\overleftarrow{r}}(G_x \left| {B_x (r))\,\,\,\,\,\,\,\,\,(r \to \infty ),} \right.$$ where B x the ball of radius r centered at x, is a finite subtree (by local finiteness), and so G x is a profinite group. For x, yεVX, G x and G y are commensurable: If d(x,y)=r then G x ∩ G y contains \(Ker(G_x \,\xrightarrow{{res}}\,Aut(B_x (r)))\).KeywordsTree LatticeQuotient GraphDeck TransformationProfinite GroupLocal FinitenessThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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