交叉布线的Lighter群的结构
Structure of Cross-wired Lamplighter Groups
摘要：
我们回答了Cornulier，Fisher和Kashyap提出的一个问题，证明了对于$\text{Isom}(\text{DL}(n, n))$的闭余紧子群$Γ$不包含在$\text{Isom}^+(\text{DL}(n, n))$中，序列$1 \to H \to Γ\to D_\infty \to 1$分裂，其中$H$是唯一的开正规子群，使得$Γ/H \cong D_\infty$。
英文摘要：
We answer a question posed by Cornulier, Fisher, and Kashyap, proving that for a closed cocompact subgroup $Γ$ of $\text{Isom}(\text{DL}(n, n))$ not contained in $\text{Isom}^+(\text{DL}(n, n))$, the sequence $1 \to H \to Γ\to D_\infty \to 1$ splits, where $H$ is the unique open normal subgroup such that $Γ/H \cong D_\infty$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
