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
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 \(Ker(G_x \,\xrightarrow{{res}}\,Aut(B_x (r)))\).
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© 2001 Birkhäuser Boston
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Bass, H., Lubotzky, A. (2001). Tree Lattices. In: Tree Lattices. Progress in Mathematics, vol 176. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-2098-5_4
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DOI: https://doi.org/10.1007/978-1-4612-2098-5_4
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7413-1
Online ISBN: 978-1-4612-2098-5
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