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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.11244 |
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| _version_ | 1866915065302614016 |
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| author | Han, Suzhen Liu, Qing |
| author_facet | Han, Suzhen Liu, Qing |
| contents | We prove that stable subgroups of Morse local-to-global groups exhibit a growth gap. That is, the growth rate of an infinite-index stable subgroup is strictly less than the growth rate of the ambient Morse local-to-global group. This generalizes a result of Cordes, Russell, Spriano, and Zalloum in the sense that we removed the additional torsion-free or residually finite assumptions. The Morse local-to-global groups are a very broad class of groups, including mapping class groups, CAT(0) groups, closed $3$-manifold groups, certain relatively hyperbolic groups, virtually solvable groups, etc. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_11244 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Growth Rate Gap for Stable Subgroups Han, Suzhen Liu, Qing Group Theory 20F65, 20F67 We prove that stable subgroups of Morse local-to-global groups exhibit a growth gap. That is, the growth rate of an infinite-index stable subgroup is strictly less than the growth rate of the ambient Morse local-to-global group. This generalizes a result of Cordes, Russell, Spriano, and Zalloum in the sense that we removed the additional torsion-free or residually finite assumptions. The Morse local-to-global groups are a very broad class of groups, including mapping class groups, CAT(0) groups, closed $3$-manifold groups, certain relatively hyperbolic groups, virtually solvable groups, etc. |
| title | Growth Rate Gap for Stable Subgroups |
| topic | Group Theory 20F65, 20F67 |
| url | https://arxiv.org/abs/2412.11244 |