{"title":"On weak commutativity in 𝑝-groups","authors":"R. Bastos, E. de Melo, R. de Oliveira, C. Monetta","doi":"10.1515/jgth-2022-0165","DOIUrl":null,"url":null,"abstract":"Abstract The weak commutativity group χ ( G ) \\chi(G) is generated by two isomorphic groups 𝐺 and G φ G^{\\varphi} subject to the relations [ g , g φ ] = 1 [g,g^{\\varphi}]=1 for all g ∈ G g\\in G . We present new bounds for the exponent of χ ( G ) \\chi(G) and its sections, when 𝐺 is a finite 𝑝-group.","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":"22 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Group Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2022-0165","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The weak commutativity group χ ( G ) \chi(G) is generated by two isomorphic groups 𝐺 and G φ G^{\varphi} subject to the relations [ g , g φ ] = 1 [g,g^{\varphi}]=1 for all g ∈ G g\in G . We present new bounds for the exponent of χ ( G ) \chi(G) and its sections, when 𝐺 is a finite 𝑝-group.
期刊介绍：
The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.
Topics:
Group Theory-
Representation Theory of Groups-
Computational Aspects of Group Theory-
Combinatorics and Graph Theory-
Algebra and Number Theory
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