拼图组构造新例
New Examples from the Jigsaw Groups Construction
摘要：
一个伪模群是一个离散子群$Γ\leq PGL(2,\mathbb{Q})$，它不能与$PSL(2,\mathbb{Z})$交换，但它的尖点集精确地为$\mathbb{Q}\cup\{\infty\}$。Long和Reid证明了这种群的存在。后来，Lou，Tan和Vo构造了两个无限族的不可分解的伪模群，他们称之为拼图群。在本文中，我们构造了一个新的无限族的不可分解的伪模群通过这种拼图结构。我们还发现，无穷多个最简单的拼图组不是pseudomodular，提供了部分回答上述作者提出的问题。
英文摘要：
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.
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