{"title":"On commuting probabilities in finite groups and rings","authors":"Martin Jur'avs, M. Ursul","doi":"10.13069/jacodesmath.1056492","DOIUrl":null,"url":null,"abstract":"We show that the set of all commuting probabilities in finite rings is a subset of the set of all commuting probabilities in finite nilpotent groups of class $\\le2$. We believe that these two sets are equal; we prove they are equal, when restricted to groups and rings with odd number of elements.","PeriodicalId":37029,"journal":{"name":"Journal of Algebra Combinatorics Discrete Structures and Applications","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-10-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra Combinatorics Discrete Structures and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.13069/jacodesmath.1056492","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 1
Abstract
We show that the set of all commuting probabilities in finite rings is a subset of the set of all commuting probabilities in finite nilpotent groups of class $\le2$. We believe that these two sets are equal; we prove they are equal, when restricted to groups and rings with odd number of elements.
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