Free-by-cyclic groups are equationally Noetherian
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914177874919424 |
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| author | Kudlinska, Monika Valiunas, Motiejus |
| author_facet | Kudlinska, Monika Valiunas, Motiejus |
| contents | A group $G$ is said to be equationally Noetherian if every system of equations in $G$ is equivalent to a finite subsystem. We show that all free-by-cyclic groups are equationally Noetherian. As a corollary, we deduce that the set of exponential growth rates of a free-by-cyclic group is well ordered. Along the way, we prove that free-by-cyclic groups with polynomially growing monodromies of infinite order admit non-elementary 4-acylindrical actions on trees. We show that the splittings arising from the improved relative train track machinery of Bestvina-Feighn-Handel are 2-acylindrical when the growth is at least quadratic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_08809 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Free-by-cyclic groups are equationally Noetherian Kudlinska, Monika Valiunas, Motiejus Group Theory 20F70, 20E36, 20E08, 20F69 A group $G$ is said to be equationally Noetherian if every system of equations in $G$ is equivalent to a finite subsystem. We show that all free-by-cyclic groups are equationally Noetherian. As a corollary, we deduce that the set of exponential growth rates of a free-by-cyclic group is well ordered. Along the way, we prove that free-by-cyclic groups with polynomially growing monodromies of infinite order admit non-elementary 4-acylindrical actions on trees. We show that the splittings arising from the improved relative train track machinery of Bestvina-Feighn-Handel are 2-acylindrical when the growth is at least quadratic. |
| title | Free-by-cyclic groups are equationally Noetherian |
| topic | Group Theory 20F70, 20E36, 20E08, 20F69 |
| url | https://arxiv.org/abs/2407.08809 |