https://m2.mtmt.hu/ hun 2026-05-01 12:02 JournalArticle 31892656 APPROVED true Export Date: 22 August 2022 Funding details: European Research Council, ERC, 648017 Funding details: Mount Allison University, MTA Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K109684 Funding text 1: Received by the editors February 4, 2020, and, in revised form, November 20, 2020, and December 29, 2020. 2020 Mathematics Subject Classification. Primary 20E08, 20B27, 05C25, 22D40. The first author was partially supported by the MTA Rényi Institute Lendület Limits of Structures Research Group. The second author was supported by the ERC Consolidator Grant 648017. Both authors were partially supported by the Hungarian National Research, Development and Innovation Office, NKFIH grant K109684. 0 false 2025-12-30T19:36:45.829+0000 2023-10-17T11:58:40.255+0000 2021-02-26T08:35:27.309+0000 true 10015168 Szakonyi Erzsebet /api/admin/10015168 Admin true 10015168 2025-02-27T12:26:06.454+0000 2025-02-27T12:26:06.454+0000 true false true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle true 10000059 Article true 24 24 /api/publicationtype/24 PublicationType 1 true 24 JournalArticle /api/subtype/10000059 Szakcikk SubType 101 true 10000059 true 1 /api/category/1 Category true 1 Bencs, Ferenc Invariant random subgroups of groups acting on rooted trees true true /api/journal/4214 REVIEWED true false 4214 false 4214 true 0002-9947 1088-6850 Journal FOREIGN 374 7011 7040 7011 30 2021 We investigate invariant random subgroups in groups acting on rooted trees. Let Alt(f) (T) be the group of finitary even automorphisms of the d-ary rooted tree T. We prove that a nontrivial ergodic invariant random subgroup (IRS) of Alt(f) (T) that acts without fixed points on the boundary of T contains a level stabilizer, in particular it is the random conjugate of a finite index subgroup.Applying the technique to branch groups we prove that an ergodic IRS in a finitary regular branch group contains the derived subgroup of a generalized rigid level stabilizer. We also prove that every weakly branch group has continuum many distinct atomless ergodic IRS's. This extends a result of Benli, Grigorchuk and Nagnibeda who exhibit a group of intermediate growth with this property. 2021 true true true false false GREEN 2025-12-30 true http://real.mtak.hu/138968 6 0 2 2 0 2 2 2 2 2 2 2 2 5 1 0 6 5 2 2 0 2 2 Folyóiratcikk Journal Article 24 2 Könyvrészlet Chapter in Book 25 0 Könyv Book 23 0 Egyéb konferenciaközlemény Conference paper 31 0 Egyéb konferenciakötet Conference proceedings 32 0 Oltalmi formák Protection forms 26 0 Disszertáció Thesis 28 2 Egyéb Miscellaneous 29 2 Alkotás Achievement 22 0 Kutatási adat Research data 33 0 Folyóiratcikk Journal Article 24 0 0 0 Könyvrészlet Chapter in Book 25 0 0 0 Könyv Book 23 0 0 0 Egyéb konferenciaközlemény Conference paper 31 0 0 0 Egyéb konferenciakötet Conference proceedings 32 0 0 0 Oltalmi formák Protection forms 26 0 0 0 Disszertáció Thesis 28 0 0 0 Egyéb Miscellaneous 29 0 0 0 Alkotás Achievement 22 0 0 0 Kutatási adat Research data 33 0 0 0 2018 0 1 0 1 0 2019 0 1 1 1 1 2020 0 0 0 0 0 2021 0 1 1 1 1 2022 0 0 0 0 0 2023 0 2 2 2 2 2024 0 0 0 0 0 2025 0 1 1 1 1 D1 false 10076734 false false false 2021-05-27T07:35:39.112+0000 Csoportok és gráfok - Lendület (HRN RAMKI); 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margin-bottom: 0;"><u>Megjegyzés</u>: Export Date: 22 August 2022 Funding details: European Research Council, ERC, 648017 Funding details: Mount Allison University, MTA Funding details: Nemzeti Kutatási Fejlesztési és Innovációs Hivatal, NKFIH, K109684 Funding text 1: Received by the editors February 4, 2020, and, in revised form, Novemb...</pre> </div></div>