{"title":"A note on the conjugacy problem for finite Sylow subgroups of linear pseudofinite groups","authors":"Pinar Uugurlu","doi":"10.3906/mat-1604-11","DOIUrl":null,"url":null,"abstract":"We prove the conjugacy of Sylow $2$-subgroups in pseudofinite $\\mathfrak{M}_c$ (in particular linear) groups under the assumption that there is at least one finite Sylow $2$-subgroup. We observe the importance of the pseudofiniteness assumption by analyzing an example of a linear group with non-conjugate finite Sylow $2$-subgroups which was constructed by Platonov.","PeriodicalId":51206,"journal":{"name":"Turkish Journal of Mathematics","volume":"41 1","pages":"1458-1466"},"PeriodicalIF":0.8000,"publicationDate":"2023-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.3906/mat-1604-11","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Turkish Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3906/mat-1604-11","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
We prove the conjugacy of Sylow $2$-subgroups in pseudofinite $\mathfrak{M}_c$ (in particular linear) groups under the assumption that there is at least one finite Sylow $2$-subgroup. We observe the importance of the pseudofiniteness assumption by analyzing an example of a linear group with non-conjugate finite Sylow $2$-subgroups which was constructed by Platonov.
期刊介绍:
The Turkish Journal of Mathematics is published electronically 6 times a year by the Scientific and Technological Research
Council of Turkey (TÜBİTAK) and accepts English-language original research manuscripts in the field of mathematics.
Contribution is open to researchers of all nationalities.