论文标题
D型Coxeter组的基础定理的概括
Generalization of the basis theorem for the D-type Coxeter groups
论文作者
论文摘要
非阿布尔群体的OGS是对有限阿贝尔群体基础的有趣概括。 OGS的定义指出，组的每个元素都有独特的演示文稿作为特定给定顺序的某些特定发电机的某些力量的产物。如果是对称组SN，则有一篇关于R. shwartz的论文，该论文证明了OGS与对称组的标准Coxeter呈现之间的牢固联系，这称为SN的标准OGS。在本文中，我们将SN的标准OGS推广到有限的经典Coxeter组DN。我们描述了DN的广义标准OGS的交换定律，并将其连接到DN元素的Coxeter长度。
The OGS for non-abelian groups is an interesting generalization of the basis of finite abelian groups. The definition of OGS states that every element of a group has a unique presentation as a product of some powers of specific generators of the group, in a specific given order. In case of the symmetric groups Sn there is a paper of R. Shwartz, which demonstrates a strong connection between the OGS and the standard Coxeter presentation of the symmetric group, which is called the standard OGS of Sn. In this paper we generalize the standard OGS of Sn to the finite classical Coxeter group Dn. We describe the exchange laws for the generalized standard OGS of Dn, and we connect it to the Coxeter length of elements of Dn.
