虚拟辫状群的特征子群和 R∞ 属性

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2024-09-06 DOI:10.1016/j.jalgebra.2024.09.002

Karel Dekimpe , Daciberg Lima Gonçalves , Oscar Ocampo

引用次数: 0

摘要

设 n≥2。让 VBn（或 VPn）表示虚辫群（或虚纯辫群），让 WBn（或 WPn）表示焊接辫群（或焊接纯辫群），让 UVBn（或 UVPn）表示无限制虚辫群（或无限制虚纯辫群）。在本文的第一部分，我们将证明，对于 n≥4，群 VPn，对于 n≥3，群 WPn 和 UVPn 分别是 VBn、WBn 和 UVBn 的特征子群。在论文的第二部分，我们证明了在 n≥2 时，虚辫群 VBn、无限制虚纯辫群 UVPn 和无限制虚辫群 UVBn 具有 R∞ 属性。作为对少数弦使用的技术的结果，我们还证明，对于 n=2、3、4，焊接辫状群 WBn 具有 R∞属性，对于 n=2，相应的纯辫状群具有 R∞属性。另一方面，当 n≥3 时，虚拟纯辫状群 VPn 和焊接纯辫状群 WPn 的 R∞ 属性是否成立还是未知数。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Characteristic subgroups and the R∞-property for virtual braid groups

Let $n \geq 2$ . Let $V B_{n}$ (resp. $V P_{n}$ ) denote the virtual braid group (resp. virtual pure braid group), let $W B_{n}$ (resp. $W P_{n}$ ) denote the welded braid group (resp. welded pure braid group) and let $U V B_{n}$ (resp. $U V P_{n}$ ) denote the unrestricted virtual braid group (resp. unrestricted virtual pure braid group). In the first part of this paper we prove that, for $n \geq 4$ , the group $V P_{n}$ and for $n \geq 3$ the groups $W P_{n}$ and $U V P_{n}$ are characteristic subgroups of $V B_{n}$ , $W B_{n}$ and $U V B_{n}$ , respectively. In the second part of the paper we show that, for $n \geq 2$ , the virtual braid group $V B_{n}$ , the unrestricted virtual pure braid group $U V P_{n}$ , and the unrestricted virtual braid group $U V B_{n}$ have the R_∞-property. As a consequence of the technique used for few strings we also prove that, for $n = 2, 3, 4$ , the welded braid group $W B_{n}$ has the R_∞-property and that for $n = 2$ the corresponding pure braid groups have the R_∞-property. On the other hand for $n \geq 3$ it is unknown if the R_∞-property holds or not for the virtual pure braid group $V P_{n}$ and the welded pure braid group $W P_{n}$ .

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.