Property $R_\infty$ for generalized Higman groups
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866913076029161472 |
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| author | Soroko, Ignat Vaskou, Nicolas |
| author_facet | Soroko, Ignat Vaskou, Nicolas |
| contents | We give a unified proof of property $R_\infty$ for the Higman groups $H_n$ ($n\ge 4$) and for their generalizations studied by Martin and Horbez--Huang. As a key step, we prove that the automorphism groups of these groups are acylindrically hyperbolic. As a byproduct, we obtain acylindrical hyperbolicity of the groups themselves. In addition, we give an independent proof, based on Delzant's lemma, of the criterion of Fournier-Facio and collaborators stating that if $\operatorname{Aut}(G)$ is acylindrically hyperbolic and $\operatorname{Inn}(G)$ is infinite, then $G$ has property $R_\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27526 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Property $R_\infty$ for generalized Higman groups Soroko, Ignat Vaskou, Nicolas Group Theory 20F65, 20E36 (Primary), 20F67, 20E45 (Secondary) We give a unified proof of property $R_\infty$ for the Higman groups $H_n$ ($n\ge 4$) and for their generalizations studied by Martin and Horbez--Huang. As a key step, we prove that the automorphism groups of these groups are acylindrically hyperbolic. As a byproduct, we obtain acylindrical hyperbolicity of the groups themselves. In addition, we give an independent proof, based on Delzant's lemma, of the criterion of Fournier-Facio and collaborators stating that if $\operatorname{Aut}(G)$ is acylindrically hyperbolic and $\operatorname{Inn}(G)$ is infinite, then $G$ has property $R_\infty$. |
| title | Property $R_\infty$ for generalized Higman groups |
| topic | Group Theory 20F65, 20E36 (Primary), 20F67, 20E45 (Secondary) |
| url | https://arxiv.org/abs/2604.27526 |