{"title":"Finite Groups with Some Bounded Codegrees","authors":"Dong Fang Yang, Yu Zeng, Heng Lv","doi":"10.1007/s10114-024-1236-0","DOIUrl":null,"url":null,"abstract":"<div><p>For a character <i>χ</i> of a finite group <i>G</i>, the number cod(<i>χ</i>)≔ ∣<i>G</i>: ker(<i>χ</i>)∣/<i>χ</i>(1) is called the codegree of <i>χ</i>. In this paper, we give a solvability criterion for a finite group <i>G</i> depending on the minimum of the ratio <i>χ</i>(1)<sup>2</sup>/cod(<i>χ</i>), when <i>χ</i> varies among the irreducible characters of <i>G</i>.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 7","pages":"1778 - 1784"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-09","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/s10114-024-1236-0","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
For a character χ of a finite group G, the number cod(χ)≔ ∣G: ker(χ)∣/χ(1) is called the codegree of χ. In this paper, we give a solvability criterion for a finite group G depending on the minimum of the ratio χ(1)2/cod(χ), when χ varies among the irreducible characters of G.
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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