## Abstract

We show that if a finitely generated group G has a nonelementary WPD action on a hyperbolic metric space X, then the number of G-conjugacy classes of X-loxodromic elements of G coming from a ball of radius R in the Cayley graph of G grows exponentially in R. As an application we prove that for N ≥ 3 the number of distinct Out(FN)-conjugacy classes of fully irreducible elements Φ from an R-ball in the Cayley graph of Out(FN) with log λ (Φ) of the order of R grows exponentially in R..

Original language | English (US) |
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Pages (from-to) | 412-421 |

Number of pages | 10 |

Journal | Bulletin of the Australian Mathematical Society |

Volume | 97 |

Issue number | 3 |

DOIs | |

State | Published - Jun 1 2018 |

## Keywords

- free group automorphisms
- loxodromic elements
- stretch factors

## ASJC Scopus subject areas

- General Mathematics

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