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St. Petersburg Mathematical Journal

ISSN 1547-7371(online) ISSN 1061-0022(print)

 
 

 

Subsystem subgroups of the group of type $ \mathrm{F}_4$ generated by short root subgroups


Author: V. Nesterov
Translated by: the author
Original publication: Algebra i Analiz, tom 31 (2019), nomer 1.
Journal: St. Petersburg Math. J. 31 (2020), 69-80
MSC (2010): Primary 20G15
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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Additional Information

V. Nesterov
Affiliation: St. Petersburg State University, 198504 St. Petersburg, Russia
Email: vl.nesterov@mail.ru

DOI: https://doi.org/10.1090/spmj/1585
Keywords: Chevalley groups, short root subgroups, subsystems subgroups
Received by editor(s): October 24, 2017
Published electronically: December 3, 2019
Article copyright: © Copyright 2019 American Mathematical Society