Subsystem subgroups of the group of type \(\mathrm{F}_4\) generated by short root subgroups. (English. Russian original) Zbl 1516.20113
St. Petersbg. Math. J. 31, No. 1, 69-80 (2020); translation from Algebra Anal. 31, No. 1, 92-107 (2019).
Summary: 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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