Abstract:
Considering the finite simple groups $F_4(2^n)$ and $G_2(p^n)$, where $p\leq3$, 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 $F_4(2^n)$, $G_2(2^n)$ and $G_2(3^n)$, 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.
Keywords:finite group of Lie type, parabolic subgroup, chief factor, unipotent radical.
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