论文标题
$ G_2，F_4，E_6，E_7 $和$ E_8 $的Coxeter组的Gröbner-Shirshov基地
Gröbner-Shirshov bases for the Coxeter groups of the types $G_2,F_4,E_6,E_7$ and $E_8$
论文作者
论文摘要
作者主要对有限的Coxeter组的Gröbner-Shirshov基地感兴趣。众所周知，有限的Coxeter组根据Coxeter-Dynkin图进行了分类。根据固定顺序，值得一提的是，群体的介绍决定了组的Gröbner-Shirshov基地。在本文中，作者重新安排发电机，将它们标记在Coxeter-dynkin图上，并简单地介绍了Gröbner-Shirshov基地，用于$ G_2，F_4，E_6 $和$ E_7 $的Coxeter组。本文还为Coxeter类型$ E_8 $的Gröbner-Shirshov基础提供了基础。
The author is mainly interest in the Gröbner-Shirshov bases of finite Coxeter groups. It is known that the finite Coxeter groups are classified in terms of Coxeter-Dynkin diagrams. Under the fixed order, it is worth mention that the presentation of group determines the Gröbner-Shirshov bases of group. In this paper, the author rearranges the generators, marks them on Coxeter-Dynkin diagrams, and gets a simple presentation of the Gröbner-Shirshov bases for Coxeter groups of types $G_2, F_4, E_6$ and $E_7$. This article also gives the Gröbner-Shirshov basis of Coxeter group of type $E_8$.
