Confined subgroups and high transitivity
Uložené v:
| Názov: | Confined subgroups and high transitivity |
|---|---|
| Autori: | Le Boudec, Adrien, Matte Bon, Nicolás |
| Prispievatelia: | Matte Bon, Nicolás, Unité de Mathématiques Pures et Appliquées (UMPA-ENSL), École normale supérieure de Lyon (ENS de Lyon), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Algèbre, géométrie, logique (AGL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), ANR-19-CE40-0008,AODynG,Algèbres d'Opérateurs et Dynamique des Groupes(2019) |
| Zdroj: | Annales Henri Lebesgue. 5:491-522 |
| Publication Status: | Preprint |
| Informácie o vydavateľovi: | Cellule MathDoc/Centre Mersenne, 2022. |
| Rok vydania: | 2022 |
| Predmety: | Classification and Properties of C*-Algebras, Action (physics), Study of Finite Groups and Graphs, Group Actions, [MATH] Mathematics [math], Group Theory (math.GR), Quantum mechanics, FOS: Mathematics, Discrete Mathematics and Combinatorics, [MATH]Mathematics [math], 20B22, 20B35, 20B07, 37B05, Mathematical Physics, Group (periodic table), Physics, Symplectic Topology and Knot Invariants, Pure mathematics, Automorphism, Automorphism group, Combinatorics, Physical Sciences, Geometry and Topology, Mathematics - Group Theory, Transitive relation, Mathematics, Finitary |
| Popis: | An action of a group G is highly transitive if G acts transitively on k-tuples of distinct points for all k≥1. Many examples of groups with a rich geometric or dynamical action admit highly transitive actions. We prove that if a group G admits a highly transitive action such that G does not contain the subgroup of finitary alternating permutations, and if H is a confined subgroup of G, then the action of H remains highly transitive, possibly after discarding finitely many points.This result provides a tool to rule out the existence of highly transitive actions, and to classify highly transitive actions of a given group. We give concrete illustrations of these applications in the realm of groups of dynamical origin. In particular we obtain the first non-trivial classification of highly transitive actions of a finitely generated group. |
| Druh dokumentu: | Article Other literature type |
| Popis súboru: | application/pdf |
| Jazyk: | English |
| ISSN: | 2644-9463 |
| DOI: | 10.5802/ahl.128 |
| DOI: | 10.60692/z90hy-kgz38 |
| DOI: | 10.48550/arxiv.2012.03997 |
| DOI: | 10.60692/4vtyq-cqa53 |
| Prístupová URL adresa: | http://arxiv.org/abs/2012.03997 https://hal.science/hal-03357490v2/document https://doi.org/10.5802/ahl.128 https://hal.science/hal-03357490v2 |
| Rights: | CC BY |
| Prístupové číslo: | edsair.doi.dedup.....8545cb2e6e216bc3a95b8ba22eee972f |
| Databáza: | OpenAIRE |
Nájsť tento článok vo Web of Science | Abstrakt: | An action of a group G is highly transitive if G acts transitively on k-tuples of distinct points for all k≥1. Many examples of groups with a rich geometric or dynamical action admit highly transitive actions. We prove that if a group G admits a highly transitive action such that G does not contain the subgroup of finitary alternating permutations, and if H is a confined subgroup of G, then the action of H remains highly transitive, possibly after discarding finitely many points.This result provides a tool to rule out the existence of highly transitive actions, and to classify highly transitive actions of a given group. We give concrete illustrations of these applications in the realm of groups of dynamical origin. In particular we obtain the first non-trivial classification of highly transitive actions of a finitely generated group. |
|---|---|
| ISSN: | 26449463 |
| DOI: | 10.5802/ahl.128 |