论文标题
广义Baumslag-Solitar群体的某些残留特性
Certain residual properties of generalized Baumslag-Solitar groups
论文作者
论文摘要
令$ g $为概括的baumslag-solitar群体，$ \ nathcal {c} $是一类组组，其中包含至少一个非单元组，并在采用$ \ prod_ {y} y} y} y} y} x_ {y} $ x，y x，y x，y x的y $ \ prod_ {y prop_ {y prop_ {y \ in y Math y Math的子组，扩展和笛卡尔产物下封闭。 $ x_ {y} $是每$ y $ y $ y \ y $的同构副本。我们给出了$ g $的标准，以作为$ \ MATHCAL {C} $ - 提供$ \ MATHCAL {C} $的组仅由定期组组成。我们还证明$ g $是无扭转的$ \ mathcal {c} $ - 如果$ \ mathcal {c} $包含一个至少一个非周期组，并且在拍摄同构图像下关闭。这些陈述概括并增强了一些已知结果。使用第一个，我们为GBS组提供标准为a）残留的nilpotent； b）无扭转的nilpotent； c）剩余的。
Let $G$ be a generalized Baumslag-Solitar group and $\mathcal{C}$ be a class of groups containing at least one non-unit group and closed under taking subgroups, extensions, and Cartesian products of the form $\prod_{y \in Y}X_{y}$, where $X, Y \in \mathcal{C}$ and $X_{y}$ is an isomorphic copy of $X$ for every $y \in Y$. We give a criterion for $G$ to be residually a $\mathcal{C}$-group provided $\mathcal{C}$ consists only of periodic groups. We also prove that $G$ is residually a torsion-free $\mathcal{C}$-group if $\mathcal{C}$ contains at least one non-periodic group and is closed under taking homomorphic images. These statements generalize and strengthen some known results. Using the first of them, we provide criteria for a GBS-group to be a) residually nilpotent; b) residually torsion-free nilpotent; c) residually free.
