{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2022-0165","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
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.
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