Raimundo Bastos , Irene N. Nakaoka , Noraí R. Rocco
{"title":"On the finiteness of the non-abelian tensor product of groups","authors":"Raimundo Bastos , Irene N. Nakaoka , 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 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 , the non-abelian q-tensor product , and homotopy pushout (cf. Section 5).
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.