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Counting growth types of automorphisms of free groups

Abstract : Given an automorphism of a free group $F_n$, we consider the following invariants: $e$ is the number of exponential strata (an upper bound for the number of different exponential growth rates of conjugacy classes); $d$ is the maximal degree of polynomial growth of conjugacy classes; $R$ is the rank of the fixed subgroup. We determine precisely which triples $(e,d,R)$ may be realized by an automorphism of $F_n$. In particular, the inequality $e\le (3n-2)/4}$ (due to Levitt-Lustig) always holds. In an appendix, we show that any conjugacy class grows like a polynomial times an exponential under iteration of the automorphism.
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Preprints, Working Papers, ...
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Contributor : Gilbert Levitt <>
Submitted on : Wednesday, January 14, 2009 - 4:51:06 PM
Last modification on : Monday, April 27, 2020 - 4:14:03 PM

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  • HAL Id : hal-00353132, version 1
  • ARXIV : 0801.4844



Gilbert Levitt. Counting growth types of automorphisms of free groups. 2009. ⟨hal-00353132⟩



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