论文标题
$ r_ \ infty $属性，用于通用可解决的鲍姆斯拉格 - 统计组的nilpotent商
The $R_\infty$ property for nilpotent quotients of generalized solvable Baumslag-Solitar groups
论文作者
论文摘要
我们说，如果扭曲的共轭类的数字$ r（φ）$对于每个自动形态$φ$ $ g $的$ r（φ）$，则$ g $具有属性$ r_ \ infty $。对于此类组，$ r_ \ infty $ -nilpotency度是最小整数$ c $，因此$ g/γ_{c+1}（g）$具有属性$ r_ \ infty $。在这项工作中，我们计算了所有通用可解决的Baumslag-Solitar-Solitar组$γ_n$的$ r_ \ infty $ niltermenty度。此外，我们计算了$γ_n$的下部中央系列，将nilpotent商$γ_{n，c} =γ_n/γ_{C+1}（γ_n）$作为有限生成的亚伯利亚群体的半导向产品，并分类了integer andeger andeger可转化矩阵的$ cod $ c $ c $ c.
We say a group $G$ has property $R_\infty$ if the number $R(φ)$ of twisted conjugacy classes is infinite for every automorphism $φ$ of $G$. For such groups, the $R_\infty$-nilpotency degree is the least integer $c$ such that $G/γ_{c+1}(G)$ has property $R_\infty$. In this work, we compute the $R_\infty$-nilpotency degree of all Generalized Solvable Baumslag-Solitar groups $Γ_n$. Moreover, we compute the lower central series of $Γ_n$, write the nilpotent quotients $Γ_{n,c}=Γ_n/γ_{c+1}(Γ_n)$ as semidirect products of finitely generated abelian groups and classify which integer invertible matrices can be extended to automorphisms of $Γ_{n,c}$.
