Minimal supplements of maximal tori in their normalizers for the groups $F_4(q)$
- Authors: Galt A.A.1,2, Staroletov A.M.1,2
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Affiliations:
- Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
- Novosibirsk State University
- Issue: Vol 86, No 1 (2022)
- Pages: 134-159
- Section: Articles
- URL: https://journal-vniispk.ru/1607-0046/article/view/142267
- DOI: https://doi.org/10.4213/im9083
- ID: 142267
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Abstract
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 $N(G,T)$.
About the authors
Alexey Albertovich Galt
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences; Novosibirsk State University
Email: galt84@gmail.com
Candidate of physico-mathematical sciences, Researcher
Alexey Mikhailovich Staroletov
Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences; Novosibirsk State University
Email: staroletov@math.nsc.ru
Candidate of physico-mathematical sciences, no status
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