Quotient-saturated groups
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866917629895114752 |
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| author | Delgado, Jordi Roy, Mallika Ventura, Enric |
| author_facet | Delgado, Jordi Roy, Mallika Ventura, Enric |
| contents | We introduce the new notion of quotient-saturation as a measure of the immensity of the quotient structure of a group. We present a sufficient condition for a finitely presented group to be quotient-saturated, and use it to deduce that non-elementary finitely presented subgroups of a hyperbolic group (in particular, non-elementary hyperbolic groups themselves) are quotient-saturated. Finally, we elaborate on the previous results to extend the scope of this property to finitely presented acylindrically hyperbolic groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_03104 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quotient-saturated groups Delgado, Jordi Roy, Mallika Ventura, Enric Group Theory 20F05 We introduce the new notion of quotient-saturation as a measure of the immensity of the quotient structure of a group. We present a sufficient condition for a finitely presented group to be quotient-saturated, and use it to deduce that non-elementary finitely presented subgroups of a hyperbolic group (in particular, non-elementary hyperbolic groups themselves) are quotient-saturated. Finally, we elaborate on the previous results to extend the scope of this property to finitely presented acylindrically hyperbolic groups. |
| title | Quotient-saturated groups |
| topic | Group Theory 20F05 |
| url | https://arxiv.org/abs/2404.03104 |