On Intersection of Primary Subgroups in the Group Aut(F4(2))

Abstract

It is proved that, in a finite group G which is isomorphic to the group of automorphisms of the Chevalley group F4(2), there are only three possibilities for ordered pairs of primary subgroups A and B with condition: A ∩ B g ̸ = 1 for any g ∈ G. We describe all ordered pairs (A, B) of such subgroups up to conjugacy in the group G and in particular, we prove that A and B are 2-groups.