Subsystem subgroups of the group of type 𝐹₄ generated by short root subgroups

Nesterov, V.

doi:10.1090/spmj/1585

Subsystem subgroups of the group of type $\mathrm {F}_4$ generated by short root subgroups
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by V. Nesterov
Translated by: the author

St. Petersburg Math. J. 31 (2020), 69-80

DOI: https://doi.org/10.1090/spmj/1585

Published electronically: December 3, 2019

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Abstract:

The subsystem subgroups of the Chevalley group of type $\mathrm {F}_4$ generated by short root subgroups are found, and the minimal number of such generating subgroups is established. In particular, it is shown that the entire group of type $F_4$ is generated by three short root subgroups, and the groups of type $\mathrm {B}_\ell$ and $\mathrm {C}_\ell$ are generated by $\ell$ short root subgroups.

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