论文标题
模块化组亚组的剪影和通用特性
Silhouettes and generic properties of subgroups of the modular group
论文作者
论文摘要
我们展示了如何计数和随机生成模块化组$ \ textsf {psl}（2，\ mathbb {z}）$的有限生成的子组。我们还证明，对于这些亚组而言，几乎疟疾和非降解性是可忽略的特性。 为实现这些结果而开发的组合方法揭示了自然地图，该图与$ \ textsf {psl}的任何有限生成的子组相关联（2，\ m athbb {z}）$一个我们称之为其silhouette的图，并且可以解释为自由有限的有限指数子组的类别$ \ textsf {psl}（2，\ mathbb {z}）$。
We show how to count and randomly generate finitely generated subgroups of the modular group $\textsf{PSL}(2,\mathbb{Z})$ of a given isomorphism type. We also prove that almost malnormality and non-parabolicity are negligible properties for these subgroups. The combinatorial methods developed to achieve these results bring to light a natural map, which associates with any finitely generated subgroup of $\textsf{PSL}(2,\mathbb{Z})$ a graph which we call its silhouette, and which can be interpreted as a conjugacy class of free finite index subgroups of $\textsf{PSL}(2,\mathbb{Z})$.
