论文标题
有限简单组的一类有效演示
A Class of Efficient Presentations of Finite Simple Groups
论文作者
论文摘要
我们展示了（等边）von dyck组$ d（2,3，n），\ n \ ge 3 $的新介绍，就两个订单$ n $的生成器而言满足三个关系的订单，其中之一是Artin的编织关系。通过删除固定发电机顺序的关系，我们获得了相应的von Dyck组的通用覆盖组。在$ n = 3，\，4，\，5 $的情况下，这些分别是有限旋转四面体，八面体和二十面体组的双重覆盖物。当$ n \ ge 6 $时，我们获得了相应的无限von dyck组的无限封面。当这些组充当双曲平面的异构体的离散组时，有趣的情况是出现的。施加合适的第三个关系，我们获得了有限简单的Chevalley类型$ A_1 $以及零星Janko Group $ j_2 $的有限简单的雪佛莉组的（高效）演示。
We exhibit a new presentation of the (equilateral) Von Dyck groups $D(2,3,n), \ n\ge 3$, in terms of two generators of order $n$ satisfying three relations, one of which is Artin's braid relation. By dropping the relation which fixes the order of the generators we obtain the universal covering groups of the corresponding Von Dyck groups. In the cases $n=3,\, 4,\,5$, these are respectively the double covers of the finite rotational tetrahedral, octahedral and icosahedral groups. When $n\ge 6$ we obtain infinite covers of the corresponding infinite Von Dyck groups. The interesting cases arise for $n\ge 7$ when these groups act as discrete groups of isometries of the hyperbolic plane. Imposing a suitable third relation we obtain a host of (efficient) presentations of finite simple Chevalley groups of type $A_1$ as well as the sporadic Janko group $J_2$.
