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The author would like to thank Adrien Le Boudec for suggesting this problem and for many useful discussions regarding this work. The author would also like to thank the anonymous referee for their valuable suggestions and helpful comments on previous versions of this text. This work was performed within the framework of the LABEX MILYON (ANR-10-LABX-0070) of Universite de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX- 0007) operated by the French National Research Agency (ANR).

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On the quasi-transitivity degree of branch groups

Publicado en:MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY (): - - 2025-08-04 (), DOI: 10.1017/S0305004125101369

Autores: Rojo, Luisa Martin

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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.

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