{"title":"Finite Solvable Groups Whose Prime Graphs have Diameter 3","authors":"Guohua Qian","doi":"10.1007/s10114-025-2021-4","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>G</i> be a finite group and <i>π</i>(<i>G</i>) be the set of prime divisors of ∣<i>G</i>∣. The prime graph Γ(<i>G</i>) of <i>G</i> is the graph with vertex set <i>π</i>(<i>G</i>), and different <i>p, q</i> ∈ <i>π</i>(<i>G</i>) are joined by an edge if and only if <i>G</i> has an element of order <i>pq</i>. In this paper, we characterize the finite solvable groups whose prime graphs have diameter 3.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"41 3","pages":"975 - 984"},"PeriodicalIF":0.9000,"publicationDate":"2025-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Sinica-English Series","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10114-025-2021-4","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Let G be a finite group and π(G) be the set of prime divisors of ∣G∣. The prime graph Γ(G) of G is the graph with vertex set π(G), and different p, q ∈ π(G) are joined by an edge if and only if G has an element of order pq. In this paper, we characterize the finite solvable groups whose prime graphs have diameter 3.
期刊介绍：
Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.
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