On intersections of primary subgroups in the group Aut(Ln(2))

Resumo

It is proved that, in a finite group G whose socle is isomorphic to L_n(2), there exist primary subgroups A and B such that the intersection of A and any subgroup conjugate to B under the action of G is nontrivial only if G is isomorphic to the group Aut(L_n(2)); in this case, A and B are 2-subgroups. All ordered pairs (A,B) of such subgroups are described.