The R ∞ R_{\infty} property for nilpotent quotients of Generalized Solvable Baumslag–Solitar groups
| Autor: | Wagner C. Sgobbi, Dalton C. Silva, Daniel Vendrúscolo |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Journal of Group Theory. |
| ISSN: | 1435-4446 1433-5883 |
| DOI: | 10.1515/jgth-2022-0129 |
| Popis: | We say a group 𝐺 has property R ∞ R_{\infty} if the number R ( φ ) R(\varphi) of twisted conjugacy classes is infinite for every automorphism 𝜑 of 𝐺. For such groups, the R ∞ R_{\infty} -nilpotency degree is the least integer 𝑐 such that G / γ c + 1 ( G ) G/\gamma_{c+1}(G) has property R ∞ R_{\infty} . In this work, we compute the R ∞ R_{\infty} -nilpotency degree of all Generalized Solvable Baumslag–Solitar groups Γ n \Gamma_{n} . Moreover, we compute the lower central series of Γ n \Gamma_{n} , write the nilpotent quotients Γ n , c = Γ n / γ c + 1 ( Γ n ) \Gamma_{n,c}=\Gamma_{n}/\gamma_{c+1}(\Gamma_{n}) as semidirect products of finitely generated abelian groups and classify which invertible integer matrices can be extended to automorphisms of Γ n , c \Gamma_{n,c} . |
| Databáze: | OpenAIRE |
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