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Preprint Number 1732
1732. Koji Fujiwara and Zlil Sela The rates of growth in a hyperbolic group E-mail: Submission date: 24 February 2020 Abstract: We study the countable set of rates of growth of a hyperbolic group with
respect to all its finite generating sets. We prove that the set is
well-ordered, and that every real number can be the rate of growth of at
most
finitely many generating sets up to automorphism of the group. We prove that
the ordinal of the set of rates of growth is at least ω^ω,
and in
case the group is a limit group (e.g., free and surface groups), it is
ω^ω. Mathematics Subject Classification: Keywords and phrases: |

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