Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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REGULAR GRAPHS AND DISCRETE SUBGROUPS OF PROJECTIVE LINEAR GROUPS

  • Chae, Hi-joon (Department of Mathematics Education Hongik University)
  • Received : 2018.03.28
  • Accepted : 2019.02.01
  • Published : 2019.02.15
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Abstract

The homothety classes of lattices in a two dimensional vector space over a nonarchimedean local field form a regular tree ${\mathcal{T}}$ of degree q + 1 on which the projective linear group acts naturally where q is the order of the residue field. We show that for any finite regular combinatorial graph of even degree q + 1, there exists a torsion free discrete subgroup ${\Gamma}$ of the projective linear group such that ${\mathcal{T}}/{\Gamma}$ is isomorphic to the graph.

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References

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