A short proof of Handel and Mosher's alternative for subgroups of Out$(F_N)$

Abstract

We give a short proof of a theorem of Handel and Mosher [21] stating that any finitely generated subgroup of Out$(F_N)$ either contains a fully irreducible automorphism, or virtually fixes the conjugacy class of a proper free factor of $F_N$, and we extend their result to non finitely generated subgroups of Out$(F_N)$.