Hereditarily just-infinite torsion groups with positive first $\ell^2$-Betti number
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866914642532499456 |
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| author | Kionke, Steffen Schesler, Eduard |
| author_facet | Kionke, Steffen Schesler, Eduard |
| contents | We present a new method to construct finitely generated, residually finite, infinite torsion groups. In contrast to known constructions, a profinite perspective enables us to control finite quotients and normal subgroups of these torsion groups. As an application, we describe the first examples of residually finite, hereditarily just-infinite groups with positive first $\ell^2$-Betti-number. In addition, we show that these groups have polynomial normal subgroup growth, which answers a question of Barnea and Schlage-Puchta. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_04542 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Hereditarily just-infinite torsion groups with positive first $\ell^2$-Betti number Kionke, Steffen Schesler, Eduard Group Theory 20E26, 20E07, 20E18, 20C05 We present a new method to construct finitely generated, residually finite, infinite torsion groups. In contrast to known constructions, a profinite perspective enables us to control finite quotients and normal subgroups of these torsion groups. As an application, we describe the first examples of residually finite, hereditarily just-infinite groups with positive first $\ell^2$-Betti-number. In addition, we show that these groups have polynomial normal subgroup growth, which answers a question of Barnea and Schlage-Puchta. |
| title | Hereditarily just-infinite torsion groups with positive first $\ell^2$-Betti number |
| topic | Group Theory 20E26, 20E07, 20E18, 20C05 |
| url | https://arxiv.org/abs/2401.04542 |