{"title":"Fusion systems realizing certain Todd modules","authors":"B. Oliver","doi":"10.1515/jgth-2022-0074","DOIUrl":null,"url":null,"abstract":"Abstract We study a certain family of simple fusion systems over finite 3-groups, ones that involve Todd modules of the Mathieu groups 2 M 12 2M_{12} , M 11 M_{11} , and A 6 = O 2 ( M 10 ) A_{6}=O^{2}(M_{10}) over F 3 \\mathbb{F}_{3} , and show that they are all isomorphic to the 3-fusion systems of almost simple groups. As one consequence, we give new 3-local characterizations of Conway’s sporadic simple groups.","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2022-0074","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
Abstract We study a certain family of simple fusion systems over finite 3-groups, ones that involve Todd modules of the Mathieu groups 2 M 12 2M_{12} , M 11 M_{11} , and A 6 = O 2 ( M 10 ) A_{6}=O^{2}(M_{10}) over F 3 \mathbb{F}_{3} , and show that they are all isomorphic to the 3-fusion systems of almost simple groups. As one consequence, we give new 3-local characterizations of Conway’s sporadic simple groups.
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