Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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ON THE SET OF CRITICAL EXPONENTS OF DISCRETE GROUPS ACTING ON REGULAR TREES

  • Kwon, Sanghoon (Department of Mathematical Education Catholic Kwandong University)
  • Received : 2018.04.05
  • Accepted : 2018.07.05
  • Published : 2019.03.01
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Abstract

We study the set of critical exponents of discrete groups acting on regular trees. We prove that for every real number ${\delta}$ between 0 and ${\frac{1}{2}}\;{\log}\;q$, there is a discrete subgroup ${\Gamma}$ acting without inversion on a (q+1)-regular tree whose critical exponent is equal to ${\delta}$. Explicit construction of edge-indexed graphs corresponding to a quotient graph of groups are given.

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References

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