Geodesic
On splitting of normalizers of maximal tori in finite groups of Lie type
Algebra i logika, Tome 62 (2023) no. 1, pp. 33-58

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Let $G$ be a finite group of Lie type, and $T$ some maximal torus of the group $G$. We bring to a close the study of the question of whether there exists a supplement for a torus $T$ in its algebraic normalizer $N(G,T)$. It is proved that any maximal torus of a group $G\in \{G_2(q),{}^2G_2(q),{}^3D_4(q)\}$ has a supplement in its algebraic normalizer. Also we consider the remaining twisted classical groups ${}^2A_n(q)$ and ${}^2D_n(q)$.
Keywords: finite group of Lie type, twisted group of Lie type, Weyl group, algebraic normalizer.
Mots-clés : maximal torus 
@article{AL_2023_62_1_a2,
     author = {A. A. Galt and A. M. Staroletov},
     title = {On splitting of normalizers of maximal tori in finite groups of {Lie} type},
     journal = {Algebra i logika},
     pages = {33--58},
     publisher = {mathdoc},
     volume = {62},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2023_62_1_a2/}
}
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A. A. Galt; A. M. Staroletov. On splitting of normalizers of maximal tori in finite groups of Lie type. Algebra i logika, Tome 62 (2023) no. 1, pp. 33-58. http://geodesic.mathdoc.fr/item/AL_2023_62_1_a2/