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Izvestiya: Mathematics, 2022, Volume 86, Issue 1, Pages 126–149
DOI: https://doi.org/10.1070/IM9083 (Mi im9083) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Minimal supplements of maximal tori in their normalizers for the groups $F_4(q)$

A. A. Gal'tab, A. M. Staroletovab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University
English version PDF (581 kB) Citations (4)
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DOI: https://doi.org/10.1070/IM9083
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 $N(G,T)$.
Keywords: finite group of Lie type $F_4$, Weyl group, maximal torus, algebraic normalizer, minimal supplement.
Funding agency Grant number
Russian Science Foundation 19-11-00039
The first author was supported by a grant from the Russian Science Foundation (project no. 19-11-00039).
Received: 06.07.2020
Revised: 15.12.2020
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2022, Volume 86, Issue 1, Pages 134–159
DOI: https://doi.org/10.4213/im9083
Bibliographic databases:
Document Type: Article
UDC: 512.542
MSC: 20G40, 20G07, 20F55
Language: English
Original paper language: Russian
Citation: A. A. Gal't, A. M. Staroletov, “Minimal supplements of maximal tori in their normalizers for the groups $F_4(q)$”, Izv. RAN. Ser. Mat., 86:1 (2022), 134–159; Izv. Math., 86:1 (2022), 126–149
Citation in format AMSBIB
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\pages 134--159
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    • This publication is cited in the following 4 articles:
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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