Mathematics > Group Theory
[Submitted on 23 Dec 2022 (v1), last revised 7 Sep 2023 (this version, v2)]
Title:On splitting of the normalizer of a maximal torus in finite groups of Lie type
View PDFAbstract:Let $G$ be a finite group of Lie type and $T$ a maximal torus of $G$. In this paper we complete the study of the question of the existence of a complement for the torus $T$ in its algebraic normalizer $N(G,T)$. It is proved that every maximal torus of the group $G\in\{G_2(q), {}^2G_2(q), {}^3D_4(q)\}$ has a complement in its algebraic normalizer. The remaining twisted classical groups ${}^2A_n(q)$ and ${}^2D_n(q)$ are also considered.
Submission history
From: Alexey Galt [view email][v1] Fri, 23 Dec 2022 08:31:23 UTC (15 KB)
[v2] Thu, 7 Sep 2023 08:24:24 UTC (16 KB)
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