{"title":"The Essential 2-rank for Classical Groups","authors":"Jian Bei An, Yong Xu","doi":"10.1007/s10114-024-1494-x","DOIUrl":null,"url":null,"abstract":"<div><p>Let <i>G</i> be a symplectic or orthogonal group defined over a finite field with odd characteristic and let <i>D</i> ≤ <i>G</i> be a Sylow 2-subgroup. In this paper, we classify the essential 2-subgroups and determine the essential 2-rank of the Frobenius category <i>ℱ</i><sub><i>D</i></sub>(<i>G</i>). Together with the results of An-Dietrich and Cao–An–Zeng, this completes the work of essential subgroups and essential ranks of classical groups.</p></div>","PeriodicalId":50893,"journal":{"name":"Acta Mathematica Sinica-English Series","volume":"40 9","pages":"2169 - 2186"},"PeriodicalIF":0.8000,"publicationDate":"2024-05-31","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/s10114-024-1494-x","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Let G be a symplectic or orthogonal group defined over a finite field with odd characteristic and let D ≤ G be a Sylow 2-subgroup. In this paper, we classify the essential 2-subgroups and determine the essential 2-rank of the Frobenius category ℱD(G). Together with the results of An-Dietrich and Cao–An–Zeng, this completes the work of essential subgroups and essential ranks of classical groups.
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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