On the quasi-transitivity degree of branch groups

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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).

Analysis of institutional authors

Rojo, Luisa MartinCorresponding Author

August 18, 2025

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

Authors: Rojo, Luisa Martin

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Univ Autonoma Madrid, Dept Matemat, C Francisco Tomas & Valiente 7, Madrid 28049, Spain - Author

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 $Xn$ 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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Bibliometric impact. Analysis of the contribution and dissemination channel

The work has been published in the journal MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY due to its progression and the good impact it has achieved in recent years, according to the agency Scopus (SJR), it has become a reference in its field. In the year of publication of the work, 2025, it was in position , thus managing to position itself as a Q1 (Primer Cuartil), in the category .

Leadership analysis of institutional authors

There is a significant leadership presence as some of the institution’s authors appear as the first or last signer, detailed as follows: Last Author (MARTIN ROJO, LUISA).