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Tree Lattices

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

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

Keywords

Tree Lattice Quotient Graph Deck Transformation Profinite Group Local Finiteness 
These 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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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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