{"title":"A bound for the orders of centralizers of irreducible subgroups of algebraic groups","authors":"M. Liebeck","doi":"10.1515/jgth-2022-0111","DOIUrl":null,"url":null,"abstract":"Abstract We prove that if 𝐺 is a connected semisimple algebraic group of rank 𝑟, and 𝐻 is a subgroup of 𝐺 that is contained in no proper parabolic subgroup, then we have | C G ( H ) | < c r | Z ( G ) | \\lvert C_{G}(H)\\rvert<c^{r}\\lvert Z(G)\\rvert , where 𝑐 is an absolute constant ( c = 16 c=16 if all simple factors of 𝐺 are classical, and c ≤ 197 c\\leq 197 in general).","PeriodicalId":50188,"journal":{"name":"Journal of Group Theory","volume":"18 1","pages":"795 - 801"},"PeriodicalIF":0.4000,"publicationDate":"2022-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Group Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/jgth-2022-0111","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract We prove that if 𝐺 is a connected semisimple algebraic group of rank 𝑟, and 𝐻 is a subgroup of 𝐺 that is contained in no proper parabolic subgroup, then we have | C G ( H ) | < c r | Z ( G ) | \lvert C_{G}(H)\rvert
期刊介绍：
The Journal of Group Theory is devoted to the publication of original research articles in all aspects of group theory. Articles concerning applications of group theory and articles from research areas which have a significant impact on group theory will also be considered.
Topics:
Group Theory-
Representation Theory of Groups-
Computational Aspects of Group Theory-
Combinatorics and Graph Theory-
Algebra and Number Theory
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