# Growth and subgroups of Out(F_n).

• Yassine Guerch (ENS Lyon)
• Friday 24 February 2023, 13:45-14:45
• MR13.

Let $n$ be an integer and let $Out(F_n)$ be the outer automorphism group of a nonabelian free group of rank $n$. Let $[g]$ be a conjugacy class of $F_n$ and $F \in Out(F_n)$. The class $[g]$ has exponential growth under iteration of $F$ if the word length (for a given basis of $F_n$) of $F^m([g])$ grows exponentially fast with $m$. We will present a structure result for subgroups of $Out(F_n)$ which shows that, given a subgroup $H$ of $Out(F_n)$, there exist generic elements of $H$ which encapture the exponential growth of every element of $H$.

This talk is part of the Geometric Group Theory (GGT) Seminar series.