Abstract:
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 groups $^2F_4(2^{2n+1})$ and $B_l(2^n)$. In present paper, such a description is given for the group $^2F_4(2^{2n+1})$. We prove a theorem in which, for every parabolic maximal subgroup of $^2F_4(2^{2n+1})$, a fragment of the chief series involved in the unipotent radical of this 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, chief factor, unipotent radical, strong version of the Sims conjecture.