论文标题
相对双曲线的几乎特殊组的仔细完成
The profinite completion of relatively hyperbolic virtually special groups
论文作者
论文摘要
我们从涂鸦完成方面给出了相对双曲线的表征。我们还证明了对相对双曲线实际上紧凑的特殊组$ g $的profinite完成$ \ hat g $子组的山雀替代方案，并完全描述了有限生成的pro-p $ p $ subgroups $ \ hat g $。这适用于双曲算术歧管的基本组的详细完成。我们推断出所有有限生成的$ P $ p $子组的标准算术晶格的$ so（n，1）$都是免费pro- $ p $。
We give a characterization of toral relatively hyperbolic virtually special groups in terms of the profinite completion. We also prove a Tits alternative for subgroups of the profinite completion $\hat G$ of a relatively hyperbolic virtually compact special group $G$ and completely describe finitely generated pro-$p$ subgroups of $\hat G$. This applies to the profinite completion of the fundamental group of a hyperbolic arithmetic manifold. We deduce that all finitely generated pro-$p$ subgroups of the congruence kernel of a standard arithmetic lattice of $SO(n,1)$ are free pro-$p$.
