Random subgroups of branch groups
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918131562184704 |
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| author | Fariña-Asategui, Jorge Radi, Santiago |
| author_facet | Fariña-Asategui, Jorge Radi, Santiago |
| contents | We show that independent Haar-random elements in a super strongly fractal branch profinite group generate a free subgroup acting freely on the boundary of the tree. This improves a previous result of Abért (2005) for weakly branch profinite groups, where independent random elements were shown to generate free subgroups acting only almost freely on the boundary. Our result also generalizes the analogous result of Abért and Virág (2005) for iterated wreath products. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20082 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Random subgroups of branch groups Fariña-Asategui, Jorge Radi, Santiago Group Theory Primary: 20E08, 20E18, Secondary: 28C10 We show that independent Haar-random elements in a super strongly fractal branch profinite group generate a free subgroup acting freely on the boundary of the tree. This improves a previous result of Abért (2005) for weakly branch profinite groups, where independent random elements were shown to generate free subgroups acting only almost freely on the boundary. Our result also generalizes the analogous result of Abért and Virág (2005) for iterated wreath products. |
| title | Random subgroups of branch groups |
| topic | Group Theory Primary: 20E08, 20E18, Secondary: 28C10 |
| url | https://arxiv.org/abs/2508.20082 |