Abstract Let S B n be the singular braid group generated by braid generators σ i and singular braid generators τ i , 1 ≤ i ≤ n − 1 . Let S T n denote the group that is the kernel of the homomorphism that maps, for each i, σ i to the cyclic permutation ( i , i + 1 ) and τ i to 1. In this paper we investigate the group S T 3 . We obtain a presentation for S T 3 . We prove that S T 3 is isomorphic to the singular pure braid group S P 3 on 3 strands. We also prove that the group S T 3 is semi-direct product of a subgroup H and an infinite cyclic group, where the subgroup H is an HNN-extension of Z 2 ⁎ Z 2 .

中文翻译：

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3-strand Singular Braid Group的一些分解

摘要 设SB n 为由编织发生器σ i 和奇异编织发生器τ i 产生的奇异编织群，1 ≤ i ≤ n − 1 。让 ST n 表示作为同态核的群，对于每个 i，σ i 映射到循环置换 ( i , i + 1 ) 和 τ i 到 1。在本文中，我们研究群 ST 3 。我们获得了 ST 3 的演示文稿。我们证明 ST 3 同构于 3 股上的奇异纯编织群 SP 3。我们还证明群 ST 3 是子群 H 和无限循环群的半直积，其中子群 H 是 Z 2 ⁎ Z 2 的 HNN 扩展。