{"title":"关于有限群的循环子群数目的一个结果","authors":"M. Tarnauceanu","doi":"10.3792/PJAA.96.018","DOIUrl":null,"url":null,"abstract":"Let $G$ be a finite group, $L_1(G)$ be its poset of cyclic subgroups and consider the quantity $\\alpha(G)=\\frac{|L_1(G)|}{|G|}$. The aim of this paper is to study the class $\\cal{C}$ of finite nilpotent groups having $\\alpha(G)=\\frac{3}{4}$. We show that if $G$ belongs to this class, then it is a 2-group satisfying certain conditions. Also, we study the appartenance of some classes of finite groups to $\\cal{C}$.","PeriodicalId":8427,"journal":{"name":"arXiv: Group Theory","volume":"72 4 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2020-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A result on the number of cyclic subgroups of a finite group\",\"authors\":\"M. Tarnauceanu\",\"doi\":\"10.3792/PJAA.96.018\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $G$ be a finite group, $L_1(G)$ be its poset of cyclic subgroups and consider the quantity $\\\\alpha(G)=\\\\frac{|L_1(G)|}{|G|}$. The aim of this paper is to study the class $\\\\cal{C}$ of finite nilpotent groups having $\\\\alpha(G)=\\\\frac{3}{4}$. We show that if $G$ belongs to this class, then it is a 2-group satisfying certain conditions. Also, we study the appartenance of some classes of finite groups to $\\\\cal{C}$.\",\"PeriodicalId\":8427,\"journal\":{\"name\":\"arXiv: Group Theory\",\"volume\":\"72 4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-03-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3792/PJAA.96.018\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3792/PJAA.96.018","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A result on the number of cyclic subgroups of a finite group
Let $G$ be a finite group, $L_1(G)$ be its poset of cyclic subgroups and consider the quantity $\alpha(G)=\frac{|L_1(G)|}{|G|}$. The aim of this paper is to study the class $\cal{C}$ of finite nilpotent groups having $\alpha(G)=\frac{3}{4}$. We show that if $G$ belongs to this class, then it is a 2-group satisfying certain conditions. Also, we study the appartenance of some classes of finite groups to $\cal{C}$.