{"title":"论有限可解群的共轭类数","authors":"Yong Yang, Mengtian Zhang","doi":"10.1007/s00013-024-01989-9","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>p</i> be a prime that divides the order of the group <i>G</i>. We show that a finite solvable group has class number at least <i>f</i>(<i>p</i>) where <span>\\(f(p):=\\min \\{x+\\frac{p-1}{x}: x\\in \\mathbb {N}, x \\mid (p-1)\\}\\)</span>. We also obtain some applications to character degrees.</p></div>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On the number of conjugacy classes of a finite solvable group\",\"authors\":\"Yong Yang, Mengtian Zhang\",\"doi\":\"10.1007/s00013-024-01989-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Let <i>p</i> be a prime that divides the order of the group <i>G</i>. We show that a finite solvable group has class number at least <i>f</i>(<i>p</i>) where <span>\\\\(f(p):=\\\\min \\\\{x+\\\\frac{p-1}{x}: x\\\\in \\\\mathbb {N}, x \\\\mid (p-1)\\\\}\\\\)</span>. We also obtain some applications to character degrees.</p></div>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-06-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00013-024-01989-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00013-024-01989-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
我们证明一个有限可解群的类数至少是 f(p)，其中 f(p):=\min \{x+\frac{p-1}{x}: xin \mathbb {N}, x \mid (p-1)\}\).我们还得到了一些关于特征度的应用。
On the number of conjugacy classes of a finite solvable group
Let p be a prime that divides the order of the group G. We show that a finite solvable group has class number at least f(p) where \(f(p):=\min \{x+\frac{p-1}{x}: x\in \mathbb {N}, x \mid (p-1)\}\). We also obtain some applications to character degrees.
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