代数群的不可约子群的中心器阶的界

Pub Date : 2022-12-07 DOI:10.1515/jgth-2022-0111

M. Liebeck

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引用次数: 1

摘要

摘要证明了如果𝐺是一个秩为𝑟的连通半简单代数群，且𝐻是𝐺的一个子群，且该子群不包含真抛物子群，则有| C G¹(H) | < C r¹| Z¹(G) | \lvert c＿{g}(h)\rvert本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A bound for the orders of centralizers of irreducible subgroups of algebraic groups

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

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