论文标题
在3股单数纯辫子小组
On 3-strand singular pure braid group
论文作者
论文摘要
在本文中，我们研究了$ n = 2，3 $的单数纯编织组$ sp_ {n} $。我们发现这些群体的生成器，定义关系和代数结构。特别是，我们证明$ sp_ {3} $是半直接产品$ sp_ {3} = \ widetilde {v} _3 \ leftthreetimes \ Mathbb {z} $，其中$ \ widetilde {v} _3 $是基本组的hnn-Extension $ \ mathbbbbbbb $ \ mathbb^2 * \ mathbb {z}^2 $和环状相关子组。我们证明，$ sp_3 $的中心$ z（sp_3）$是$ sp_3 $的直接因素。
In the present paper we study the singular pure braid group $SP_{n}$ for $n=2, 3$. We find generators, defining relations and the algebraical structure of these groups. In particular, we prove that $SP_{3}$ is a semi-direct product $SP_{3} = \widetilde{V}_3 \leftthreetimes \mathbb{Z}$, where $\widetilde{V}_3$ is an HNN-extension with base group $\mathbb{Z}^2 * \mathbb{Z}^2$ and cyclic associated subgroups. We prove that the center $Z(SP_3)$ of $SP_3$ is a direct factor in $SP_3$.
