Tree Lattices

  • Hyman Bass
  • Alexander Lubotzky
Part of the Progress in Mathematics book series (PM, volume 176)


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, VX, G x and G y are commensurable: If d(x,y)=r then G x G y contains \(Ker(G_x \,\xrightarrow{{res}}\,Aut(B_x (r)))\).


Tree Lattice Quotient Graph Deck Transformation Profinite Group Local Finiteness 
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Copyright information

© Birkhäuser Boston 2001

Authors and Affiliations

  • Hyman Bass
    • 1
  • Alexander Lubotzky
    • 2
  1. 1.Department of MathematicsUniversity of Michigan Ann ArborUSA
  2. 2.Department of Mathematics HebrewUniversity JerusalemIsrael

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