论文标题
将小组限制在一致的右角Artin组上
Limit groups over coherent right-angled Artin groups
论文作者
论文摘要
定义了一个新的组$ \ MATHCAL {C} $，包含所有相干RAAG和所有相对双曲线组。结果表明，对于类$ \ mathcal {c} $中的组$ g $，$ \ mathbb {z} [t] $ - 指数组$ g^{\ mathbb {z} [t] [t]} $可能被构造为迭代的centraliseser扩展。利用这个事实，证明$ g^{\ mathbb {z} [t]} $是完全残留的$ g $（即它具有与$ g $相同的通用理论），因此其有限生成的子组是$ g $的限制组。如果$ \ mathbb {g} $是一个连贯的raag，则匡威也可以 - $ \ mathbb {g} $嵌入到$ \ mathbb {g}^{\ mathbb {Z} [z} [t]} $上的任何极限组。此外，事实证明，限制组超过$ \ mathbb {g} $是有限呈现，连贯和cat $（0）$的，因此特别是有可解决的单词和共轭问题。
A new class of groups $\mathcal{C}$, containing all coherent RAAGs and all toral relatively hyperbolic groups, is defined. It is shown that, for a group $G$ in the class $\mathcal{C}$, the $\mathbb{Z}[t]$-exponential group $G^{\mathbb{Z}[t]}$ may be constructed as an iterated centraliser extension. Using this fact, it is proved that $G^{\mathbb{Z}[t]}$ is fully residually $G$ (i.e. it has the same universal theory as $G$) and so its finitely generated subgroups are limit groups over $G$. If $\mathbb{G}$ is a coherent RAAG, then the converse also holds - any limit group over $\mathbb{G}$ embeds into $\mathbb{G}^{\mathbb{Z}[t]}$. Moreover, it is proved that limit groups over $\mathbb{G}$ are finitely presented, coherent and CAT$(0)$, so in particular have solvable word and conjugacy problems.
