This work demonstrates that branch groups cannot act quasi-2-transitively on infinite sets, suggesting limitations in their structural properties.
An action of a group G on a set X is said to be quasi- n -transitive if the diagonal action of G on Xⁿ 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.
No takes yet. Share an insight, caveat, or question.
Dominik Francoeur (2025) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: