V.V. Korableva. On chief factors of parabolic maximal subgroups of the group $B_l(2^n)$ ... P. 110-115

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

REFERENCES

1.   Azad H., Barry M., Seitz G. On the structure of parabolic subgroup. Com. in Algebra, 1990, vol. 18, no. 2, pp. 551–562. doi: 10.1080/00927879008823931 

2.   Bourbaki N. Groupes et algebres de Lie, Chaps. VII-VIII. Berlin; Heidelberg: Springer-Verlag, 2006, 265 p. doi: 10.1007/978-3-540-33977-9 . Translated to Russian under the title Gruppy i algebry Li, glavy VII-VIII. Moscow: Mir Publ., 1978, 342 p.

3.   Carter R.W. Simple groups of Lie type. London: John Wiley and Sons, 1972, 332 p. ISBN: 0471137359 .

4.   Kondrat’ev A.S., Trofimov V.I. Vertex stabilizers of vertices of graphs with primitive automorphism groups and a strong version of the Sims conjecture. In: Proc. Conf. “Groups St Andrews 2017 in Birmingham”. London Math. Soc. Note Ser., vol. 455. Cambridge: Cambridge Univ. Press, 2019, pp. 419–426. doi: 10.1017/9781108692397.017 

5.   Korableva V.V. On the chief factors of parabolic maximal subgroups of finite simple groups of normal Lie type. Sib. Math. J., 2014, vol. 55, no. 4, pp. 622–638. doi: 10.1134/S0037446614040053 

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.