This study continues the author's previous papers, where a refined description of the chief factors of a parabolic maximal subgroup involved in its unipotent radical was obtained for all (normal and twisted) finite simple groups of Lie type except for the group $B_l(2^n)$. In present paper, such a description is given the group $B_l(2^n)$. For every parabolic maximal subgroup of $B_l(2^n)$, a fragment of its chief series involved in the unipotent radical of this parabolic subgroup is given. Generators of the corresponding chief factors are presented in a table.
Keywords: finite simple group, group of Lie type, parabolic maximal subgroup, unipotent radical, chief factor, strong version of Sims conjecture
Received October 5, 2020
Revised December 21, 2020
Accepted January 11, 2021
Funding Agency: This work was supported by the Russian Foundation for Basic Research (project no. 20-01-00456).
Vera Vladimirovna Korableva, Dr. Phys.-Math. Sci., Chelyabinsk State University, Chelyabinsk, 454000 Russia; N.N. Krasovskii Institute of Mathematics and Mechanics of the Ural Branch of the Russian of the Academy of Sciences, Yekaterinburg, 620108 Russia, e-mail: vvk@csu.ru
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Cite this article as: V.V. Korableva. On chief factors of parabolic maximal subgroups of the group $B_l(2^n)$, Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2021, vol. 27, no. 1, pp. 110–115.
