{"title":"关于𝑝-groups的弱交换性","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":"{\"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}","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
摘要
摘要对所有G∈G G \in G，由两个同构群𝐺和G φ G^ {\varphi}根据关系[G, G φ]=1 [G, G^ {\varphi}]=1生成弱交换群χ≠(G) \chi (G)。当𝐺是有限的𝑝-group时，我们给出了χ¹(G) \chi (G)的指数及其截面的新边界。
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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