{"title":"关于有限群连接图的一些结果","authors":"Zahara Bahrami, B. Taeri","doi":"10.22108/IJGT.2020.123287.1625","DOIUrl":null,"url":null,"abstract":"Let $G$ be a finite group which is not cyclic of prime power order. The join graph $Delta(G)$ of $G$ is a graph whose vertex set is the set of all proper subgroups of $G$, which are not contained in the Frattini subgroup $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $G=langle H, Krangle$. Among other results, we show that if $G$ is a finite cyclic group and $H$ is a finite group such that $Delta(G)congDelta(H)$, then $H$ is cyclic. Also we prove that $Delta(G)congDelta(A_5)$ if and only if $Gcong A_5$.","PeriodicalId":43007,"journal":{"name":"International Journal of Group Theory","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2021-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Some results on the join graph of finite groups\",\"authors\":\"Zahara Bahrami, B. Taeri\",\"doi\":\"10.22108/IJGT.2020.123287.1625\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $G$ be a finite group which is not cyclic of prime power order. The join graph $Delta(G)$ of $G$ is a graph whose vertex set is the set of all proper subgroups of $G$, which are not contained in the Frattini subgroup $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $G=langle H, Krangle$. Among other results, we show that if $G$ is a finite cyclic group and $H$ is a finite group such that $Delta(G)congDelta(H)$, then $H$ is cyclic. Also we prove that $Delta(G)congDelta(A_5)$ if and only if $Gcong A_5$.\",\"PeriodicalId\":43007,\"journal\":{\"name\":\"International Journal of Group Theory\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2021-12-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Group Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22108/IJGT.2020.123287.1625\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22108/IJGT.2020.123287.1625","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Let $G$ be a finite group which is not cyclic of prime power order. The join graph $Delta(G)$ of $G$ is a graph whose vertex set is the set of all proper subgroups of $G$, which are not contained in the Frattini subgroup $G$ and two distinct vertices $H$ and $K$ are adjacent if and only if $G=langle H, Krangle$. Among other results, we show that if $G$ is a finite cyclic group and $H$ is a finite group such that $Delta(G)congDelta(H)$, then $H$ is cyclic. Also we prove that $Delta(G)congDelta(A_5)$ if and only if $Gcong A_5$.
期刊介绍：
International Journal of Group Theory (IJGT) is an international mathematical journal founded in 2011. IJGT carries original research articles in the field of group theory, a branch of algebra. IJGT aims to reflect the latest developments in group theory and promote international academic exchanges.
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