Geometriae Dedicata

, Volume 118, Issue 1, pp 1–21

Counting Overlattices in Automorphism Groups of Trees



We give an upper bound for the number uΓ(n) of “overlattices” in the automorphism group of a tree, containing a fixed lattice Γ with index n. For an example of Γ in the automorphism group of a 2p-regular tree whose quotient is a loop, we obtain a lower bound of the asymptotic behavior as well.


groups acting on trees graph of groups 

Mathematics Subject Classification (2000)

20F65 20E08 


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Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Yale UniversityNew HavenU.S.A
  2. 2.ENS Paris, UMR 8553Paris Cedex 05France

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