On the Chief Factors of Parabolic Maximal Subgroups of Special Finite Simple Groups of Exceptional Lie Type

Abstract

Considering the finite simple groups F₄(2ⁿ) and G₂(pⁿ), where p ≤ 3, we give a description of the chief factors of a parabolic maximal subgroup involved in its unipotent radical. For every parabolic maximal subgroup of the groups F₄(2ⁿ), G₂(2ⁿ), and G₂(3ⁿ), we give the fragment of its chief series that involves in the unipotent radical of this parabolic subgroup. The generators of the corresponding chief factors are presented in three tables.