论文标题
拼图群的新示例
New Examples from the Jigsaw Groups Construction
论文作者
论文摘要
伪模块化组是一个离散的子组$γ\ leq pgl（2，\ mathbb {q}）$，与$ psl（2，\ mathbb {z}）$不符，并且cusp设置了精确的$ \ \ \ \ \ \ \ m ive {q} \ cup \ cup \ cup \ cup \ {朗和里德证明了这样的群体的存在。后来，Lou，Tan和Vo建立了两个无限型假导组的无限家族，他们称之为拼图群。在本文中，我们构建了一个通过这种拼图结构获得的新的无限型假导群的家族。我们还发现，许多最简单的拼图群都不是伪模块化，为上述作者提出的问题提供了部分答案。
A pseudomodular group is a discrete subgroup $Γ\leq PGL(2,\mathbb{Q})$ which is not commensurable with $PSL(2,\mathbb{Z})$ and has cusp set precisely $\mathbb{Q}\cup\{\infty\}$. The existence of such groups was proved by Long and Reid. Later, Lou, Tan and Vo constructed two infinite families of non-commensurable pseudomodular groups which they called jigsaw groups. In this paper we construct a new infinite family of non-commensurable pseudomodular groups obtained via this jigsaw construction. We also find that infinitely many of the simplest jigsaw groups are not pseudomodular, providing a partial answer to questions posed by the aforementioned authors.
