论文标题
1 cusped Picard模块化组中的扭转
Torsion in 1-cusped Picard modular groups
论文作者
论文摘要
我们提出了一种系统的有效方法，用于构建PICARD模块化组$ PU（2,1，\ MATHCAL {O} _D）$的动作的粗糙基本域，其中$ \ Mathcal {o} _D $具有第一类，即$ D = 1,2,3,3,3,3,119,119,19,19,19,43,43,67,1633 $。这些计算可以快速执行至值$ d = 19 $。作为这种方法的应用，我们将扭转元素的共轭类别分类，推断出组的简短演示，并构建小索引的整齐亚组。
We present a systematic effective method to construct coarse fundamental domains for the action of the Picard modular groups $PU(2,1,\mathcal{O}_d)$ where $\mathcal{O}_d$ has class number one, i.e. $d=1,2,3,7,11,19,43,67,163$. The computations can be performed quickly up to the value $d=19$. As an application of this method, we classify conjugacy classes of torsion elements, deduce short presentations for the groups, and construct neat subgroups of small index.
