On algebraic normalisers of maximal tori in simple groups of Lie type

Pub Date : 2024-05-16 DOI:10.1515/jgth-2023-0070

Anton A. Baykalov

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引用次数: 0

Abstract

Let 𝐺 be a finite simple group of Lie type and let 𝑇 be a maximal torus of 𝐺. It is well known that if the defining field of 𝐺 is large enough, then the normaliser of 𝑇 in 𝐺 is equal to the algebraic normaliser N ⁢ ( G , T )

N(G,T)

. We identify explicitly all the cases when N G ⁢ ( T )

N_{G}(T)

is not equal to N ⁢ ( G , T )

N(G,T)

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论李型简单群中最大环的代数归一化

设𝐺是一个有限李型简单群，设𝑇是𝐺的最大环。众所周知，如果𝐺 的定义域足够大，那么𝐺 中𝑇 的归一化等于代数归一化 N ( G , T ) N(G,T)。我们明确指出 N G ( T ) N_{G}(T) 不等于 N ( G , T ) N(G,T) 的所有情况。

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