Long relators in groups generated by two parabolic elements

Rotem Yaari
{"title":"Long relators in groups generated by two parabolic elements","authors":"Rotem Yaari","doi":"arxiv-2409.08086","DOIUrl":null,"url":null,"abstract":"We find a family of groups generated by a pair of parabolic elements in which\nevery relator must admit a long subword of a specific form. In particular, this\ncollection contains groups in which the number of syllables of any relator is\narbitrarily large. This suggests that the existing methods for finding non-free\ngroups with rational parabolic generators may be inadequate in this case, as\nthey depend on the presence of relators with few syllables. Our results rely on\ntwo variants of the ping-pong lemma that we develop, applicable to groups that\nare possibly non-free. These variants aim to isolate the group elements\nresponsible for the failure of the classical ping-pong lemma.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08086","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

We find a family of groups generated by a pair of parabolic elements in which every relator must admit a long subword of a specific form. In particular, this collection contains groups in which the number of syllables of any relator is arbitrarily large. This suggests that the existing methods for finding non-free groups with rational parabolic generators may be inadequate in this case, as they depend on the presence of relators with few syllables. Our results rely on two variants of the ping-pong lemma that we develop, applicable to groups that are possibly non-free. These variants aim to isolate the group elements responsible for the failure of the classical ping-pong lemma.
由两个抛物线元素生成的组中的长关系线
我们发现了一个由一对抛物线元素生成的群族,在这个群族中,每个关联词都必须包含一个特定形式的长子词。特别是,这个集合包含的群中,任何一个关联词的音节数都是任意大的。这表明,现有的寻找具有有理抛物线生成器的非自由群的方法在这种情况下可能是不够的,因为这些方法依赖于存在音节数很少的关系子。我们的结果依赖于我们开发的适用于可能是非自由的群的乒乓稃的两个变体。这些变体旨在分离出导致经典乒乓公设失效的组元。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
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