在3股奇异纯编织群上

V. Bardakov, T. Kozlovskaya
{"title":"在3股奇异纯编织群上","authors":"V. Bardakov, T. Kozlovskaya","doi":"10.1142/s0218216520420018","DOIUrl":null,"url":null,"abstract":"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 $SP_3$.","PeriodicalId":8427,"journal":{"name":"arXiv: Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"On 3-strand singular pure braid group\",\"authors\":\"V. Bardakov, T. Kozlovskaya\",\"doi\":\"10.1142/s0218216520420018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"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 $SP_3$.\",\"PeriodicalId\":8427,\"journal\":{\"name\":\"arXiv: Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-05-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218216520420018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218216520420018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3

摘要

本文研究了$n= 2,3 $的奇异纯编织群$SP_{n}$。我们找到了生成子,定义了这些群的关系和代数结构。特别地,我们证明了$SP_{3}$是$SP_{3} = \ widdetilde {V}_3 \ left3次\mathbb{Z}$的半直积,其中$\ widdetilde {V}_3$是基群$\mathbb{Z}^2 * \mathbb{Z}^2$和循环关联子群的hnn扩展。我们证明了$SP_3$的中心$Z(SP_3)$是$SP_3$的一个直接因子。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
On 3-strand singular pure braid group
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 $SP_3$.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Galois descent of equivalences between blocks of 𝑝-nilpotent groups Onto extensions of free groups. Finite totally k-closed groups Shrinking braids and left distributive monoid Calculating Subgroups with GAP
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1