Generic groups acting on regular trees Academic Article uri icon

abstract

  • Abstract: Let $ T $ be a $ k $-regular tree ($ k\geq 3$) and $ A=\mathrm {Aut}(T) $ its automorphism group. We analyze a generic finitely generated subgroup $\Gamma $ of $ A $. We show that $\Gamma $ is free and establish a trichotomy on the closure $\overline {\Gamma} $ of $\Gamma $ in $ A. $ It turns out that $\overline {\Gamma} $ is either discrete, compact or has index at most $2$ in $ A $.

publication date

  • January 1, 2009