On quasi-2-transitive actions of branch groups

Abstract

An action of a group $G$ on a set $X$ is said to be quasi-n-transitive if the diagonal action of $G$ on $X^n$ has only finitely many orbits. We show that branch groups, a special class of groups of automorphisms of rooted trees, cannot act quasi-2-transitively on infinite sets.

18 pages

References in corpus (2)

• On maximal subgroups of infinite index in branch and weakly branch groups
• Finitely generated subgroups of lattices in PSL(2,C)