V. V. Korableva. On the chief factors of parabolic maximal subgroups of the group ${}^2F_4(2^{2n+1})$ ... P. 99-106

This article continues  the previous papers of the author where it is obtained a refined description of the chief factors of a parabolic maximal subgroup that involve in its unipotent radical for all finite simple groups of Lie type (normal and twisted) besides for the groups  ${}^2F_4(2^{2n+1})$ and $B_l(2^n)$. In present paper,  such description for ${}^2F_4(2^{2n+1})$ is given. It is proved a theorem, in which, for every parabolic maximal subgroup of the group ${}^2F_4(2^{2n+1})$, a fragment of its chief series that involves in the unipotent radical of this parabolic subgroup is given. Generating elements of the corresponding chief factors are presented in a table.

Keywords: finite simple group, group of Lie type, parabolic maximal subgroup, chief factor, unipotent radical, а strong version of the Sims conjecture.

Received November 11, 2019

Revised November 22, 2019

Accepted November 25, 2019

Vera Vladimirovna Korableva, Dr. Phys.-Math. Sci., Chelyabinsk State University, Chelyabinsk, 45400 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 the chief factors of parabolic maximal subgroups of the group ${}^2F_4(2^{2n+1})$, Trudy Instituta Matematiki i Mekhaniki URO RAN, 2019, vol. 25, no. 4, pp. 99–106.