In this paper, we study the singular pure braid group ${\mathrm{\text{SP}}}_n$ for $n=2,3$. We find generators, defining relations and the algebraical structure of these groups. In particular, we prove that ${\mathrm{\text{SP}}}_3$ is a semi-direct product ${\mathrm{\text{SP}}}_3={\tilde{V}}_3⋋\mathbb{Z}$, where ${\tilde{V}}_3$ is an HNN-extension with base group ${\mathbb{Z}}^2\ast {\mathbb{Z}}^2$ and cyclic associated subgroups. We prove that the center $Z({\mathrm{\text{SP}}}_3)$ of ${\mathrm{\text{SP}}}_3$ is a direct factor in ${\mathrm{\text{SP}}}_3$.

中文翻译：

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3股奇异纯编织群

本文研究奇异的纯编织群 ${\mathrm{\text{SP}}}_{ñ}$ 对于 $ñ=2，3$。我们找到生成器，定义这些组的关系和代数结构。特别是，我们证明${\mathrm{\text{SP}}}_3$ 是半直接产品 ${\mathrm{\text{SP}}}_3={\tilde{V}}_3⋋\mathbb{Z}$，在哪里 ${\tilde{V}}_3$ 是具有基组的HNN扩展 ${\mathbb{Z}}^2\ast {\mathbb{Z}}^2$和循环相关的子组。我们证明中心$ž（{\mathrm{\text{SP}}}_3）$ 的 ${\mathrm{\text{SP}}}_3$ 是一个直接的因素 ${\mathrm{\text{SP}}}_3$。