拟凸子群的可公度性与可分性
Commensurability and separability of quasiconvex subgroups
摘要：
我们表明，两个均匀的格子的一个规则的直角Fuchsian建筑是可折叠的，提供的室是一个多边形，至少有六个边缘。我们证明了在任意Gromovv-双曲正则直角建筑中，如果一个均匀格的拟凸子群是可分的，那么它与一个有限群的图积是可分的.对于Gromov-双曲二维Coxeter群的Davis复形的一致格，我们得到了类似的结果。我们还证明了CAT（0）平方复形的一致格被有限群的每个扩张实际上是平凡的，只要格的每个拟凸子群是可分的。
英文摘要：
We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building associated to a graph product of finite groups, a uniform lattice is commensurable with the graph product provided all of its quasiconvex subgroups are separable. We obtain a similar result for uniform lattices of the Davis complex of Gromov-hyperbolic two-dimensional Coxeter groups. We also prove that every extension of a uniform lattice of a CAT(0) square complex by a finite group is virtually trivial, provided each quasiconvex subgroup of the lattice is separable.
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