{"title":"A note on Friendly and Solitary Groups","authors":"Shubham Mittal, Gaurav Mittal, R. K. Sharma","doi":"10.24330/ieja.1260499","DOIUrl":null,"url":null,"abstract":"In this paper, we extend the notions of friendly and solitary \nnumbers to group theory and define friendly and solitary groups of \ntype-1 and type-2. We provide many examples of friendly and \nsolitary groups and study certain properties of the type-2 friends \nof cyclic $p$-groups, where $p$ is a prime number.","PeriodicalId":43749,"journal":{"name":"International Electronic Journal of Algebra","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2023-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Electronic Journal of Algebra","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24330/ieja.1260499","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: 0
Abstract
In this paper, we extend the notions of friendly and solitary
numbers to group theory and define friendly and solitary groups of
type-1 and type-2. We provide many examples of friendly and
solitary groups and study certain properties of the type-2 friends
of cyclic $p$-groups, where $p$ is a prime number.
期刊介绍：
The International Electronic Journal of Algebra is published twice a year. IEJA is reviewed by Mathematical Reviews, MathSciNet, Zentralblatt MATH, Current Mathematical Publications. IEJA seeks previously unpublished papers that contain: Module theory Ring theory Group theory Algebras Comodules Corings Coalgebras Representation theory Number theory.
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