{"title":"Numbers which are only orders of abelian or nilpotent groups","authors":"Matthew Just","doi":"10.5802/jtnb.1251","DOIUrl":null,"url":null,"abstract":"Refining a result of Erdős and Mays, we give asymptotic series expansions for the functions A(x)-C(x), the count of n≤x for which every group of order n is abelian (but not all cyclic), and N(x)-A(x), the count of n≤x for which every group of order n is nilpotent (but not all abelian).","PeriodicalId":48896,"journal":{"name":"Journal De Theorie Des Nombres De Bordeaux","volume":null,"pages":null},"PeriodicalIF":0.3000,"publicationDate":"2023-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal De Theorie Des Nombres De Bordeaux","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/jtnb.1251","RegionNum":4,"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
Refining a result of Erdős and Mays, we give asymptotic series expansions for the functions A(x)-C(x), the count of n≤x for which every group of order n is abelian (but not all cyclic), and N(x)-A(x), the count of n≤x for which every group of order n is nilpotent (but not all abelian).
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