Geodesic
Minimal supplements of maximal tori in their normalizers for the groups $F_4(q)$
Izvestiya. Mathematics , Tome 86 (2022) no. 1, pp. 126-149

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Let $G$ be a finite group of Lie type $F_4$ and $W$ the Weyl group of $G$. For every maximal torus $T$ of $G$, we find the minimal order of a supplement of $T$ in its algebraic normalizer $N(G,T)$. In particular, we find all the maximal tori that have a complement in $N(G,T)$. Let $T$ correspond to an element $w$ of $W$. We find the minimal orders of the lifts of the elements $w$ in $N(G,T)$.
Keywords: finite group of Lie type $F_4$, Weyl group, algebraic normalizer, minimal supplement.
Mots-clés : maximal torus 
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     author = {A. A. Gal't and A. M. Staroletov},
     title = {Minimal supplements of maximal tori in their normalizers for the groups $F_4(q)$},
     journal = {Izvestiya. Mathematics },
     pages = {126--149},
     publisher = {mathdoc},
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     number = {1},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2022_86_1_a3/}
}
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A. A. Gal't; A. M. Staroletov. Minimal supplements of maximal tori in their normalizers for the groups $F_4(q)$. Izvestiya. Mathematics , Tome 86 (2022) no. 1, pp. 126-149. http://geodesic.mathdoc.fr/item/IM2_2022_86_1_a3/