延伸到自由群体上。

Sebastia Mijares, E. Ventura
{"title":"延伸到自由群体上。","authors":"Sebastia Mijares, E. Ventura","doi":"10.46298/jgcc.2021.13.1.7036","DOIUrl":null,"url":null,"abstract":"An extension of subgroups $H\\leqslant K\\leqslant F_A$ of the free group of rank $|A|=r\\geqslant 2$ is called onto when, for every ambient free basis $A'$, the Stallings graph $\\Gamma_{A'}(K)$ is a quotient of $\\Gamma_{A'}(H)$. Algebraic extensions are onto and the converse implication was conjectured by Miasnikov-Ventura-Weil, and resolved in the negative, first by Parzanchevski-Puder for rank $r=2$, and recently by Kolodner for general rank. In this note we study properties of this new type of extension among free groups (as well as the fully onto variant), and investigate their corresponding closure operators. Interestingly, the natural attempt for a dual notion -- into extensions -- becomes trivial, making a Takahasi type theorem not possible in this setting.","PeriodicalId":8427,"journal":{"name":"arXiv: Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2020-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Onto extensions of free groups.\",\"authors\":\"Sebastia Mijares, E. Ventura\",\"doi\":\"10.46298/jgcc.2021.13.1.7036\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An extension of subgroups $H\\\\leqslant K\\\\leqslant F_A$ of the free group of rank $|A|=r\\\\geqslant 2$ is called onto when, for every ambient free basis $A'$, the Stallings graph $\\\\Gamma_{A'}(K)$ is a quotient of $\\\\Gamma_{A'}(H)$. Algebraic extensions are onto and the converse implication was conjectured by Miasnikov-Ventura-Weil, and resolved in the negative, first by Parzanchevski-Puder for rank $r=2$, and recently by Kolodner for general rank. In this note we study properties of this new type of extension among free groups (as well as the fully onto variant), and investigate their corresponding closure operators. Interestingly, the natural attempt for a dual notion -- into extensions -- becomes trivial, making a Takahasi type theorem not possible in this setting.\",\"PeriodicalId\":8427,\"journal\":{\"name\":\"arXiv: Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-29\",\"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/10.46298/jgcc.2021.13.1.7036\",\"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/10.46298/jgcc.2021.13.1.7036","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

当对于每个环境自由基$A'$,斯托林斯图$\Gamma_{A'}(K)$是$\Gamma_{A'}(H)$的商时,调用秩为$|A|=r\geqslant 2$的自由群的子群$H\leqslant K\leqslant F_A$的扩展。代数扩展是对的,相反的含义由Miasnikov-Ventura-Weil推测,并在否定中解决,首先由Parzanchevski-Puder对秩$r=2$,最近由Kolodner对一般秩。在这篇文章中,我们研究了这类新的自由群间扩展的性质,并研究了它们对应的闭包算子。有趣的是,对偶概念的自然尝试——扩展——变得微不足道,使得Takahasi类型定理在这种情况下不可能成立。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Onto extensions of free groups.
An extension of subgroups $H\leqslant K\leqslant F_A$ of the free group of rank $|A|=r\geqslant 2$ is called onto when, for every ambient free basis $A'$, the Stallings graph $\Gamma_{A'}(K)$ is a quotient of $\Gamma_{A'}(H)$. Algebraic extensions are onto and the converse implication was conjectured by Miasnikov-Ventura-Weil, and resolved in the negative, first by Parzanchevski-Puder for rank $r=2$, and recently by Kolodner for general rank. In this note we study properties of this new type of extension among free groups (as well as the fully onto variant), and investigate their corresponding closure operators. Interestingly, the natural attempt for a dual notion -- into extensions -- becomes trivial, making a Takahasi type theorem not possible in this setting.
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
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信