On the finiteness of the non-abelian tensor product of groups

IF 0.8 2区 数学 Q2 MATHEMATICS
Raimundo Bastos , Irene N. Nakaoka , Noraí R. Rocco
{"title":"On the finiteness of the non-abelian tensor product of groups","authors":"Raimundo Bastos ,&nbsp;Irene N. Nakaoka ,&nbsp;Noraí R. Rocco","doi":"10.1016/j.jalgebra.2024.10.008","DOIUrl":null,"url":null,"abstract":"<div><div>In this paper we provide sufficient conditions for the non-abelian tensor product <span><math><mi>G</mi><mo>⊗</mo><mi>H</mi></math></span> to be polycyclic/polycyclic-by-finite in terms of involved groups and derivative subgroups (cf. <span><span>Theorem 1.1</span></span>); we also give sufficient conditions for the (local) finiteness of the non-abelian tensor product of groups (cf. <span><span>Theorem 1.2</span></span>, <span><span>Theorem 1.5</span></span>). Furthermore, we deduce similar results for some related constructions associated to the non-abelian tensor products, such as the Schur multiplier of a pair of groups <span><math><mi>M</mi><mo>(</mo><mi>G</mi><mo>,</mo><mi>N</mi><mo>)</mo></math></span>, the non-abelian <em>q</em>-tensor product <span><math><mi>M</mi><msup><mrow><mo>⊗</mo></mrow><mrow><mi>q</mi></mrow></msup><mi>N</mi></math></span>, and homotopy pushout (cf. Section <span><span>5</span></span>).</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"664 ","pages":"Pages 251-267"},"PeriodicalIF":0.8000,"publicationDate":"2024-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324005465","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

Abstract

In this paper we provide sufficient conditions for the non-abelian tensor product GH to be polycyclic/polycyclic-by-finite in terms of involved groups and derivative subgroups (cf. Theorem 1.1); we also give sufficient conditions for the (local) finiteness of the non-abelian tensor product of groups (cf. Theorem 1.2, Theorem 1.5). Furthermore, we deduce similar results for some related constructions associated to the non-abelian tensor products, such as the Schur multiplier of a pair of groups M(G,N), the non-abelian q-tensor product MqN, and homotopy pushout (cf. Section 5).
论非阿贝尔群张量积的有限性
在本文中,我们提供了非阿贝尔张量积 G⊗H 在涉及群和导数子群方面是多环/多环-无限的充分条件(参见定理 1.1);我们还给出了群的非阿贝尔张量积的(局部)有限性的充分条件(参见定理 1.2,定理 1.5)。此外,我们还为一些与非阿贝尔张量积相关的构造推导出了类似的结果,如一对群 M(G,N) 的舒尔乘数、非阿贝尔 q 张量积 M⊗qN 以及同调推出(参见第 5 节)。
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
Journal of Algebra
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.
×
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