Abstract
It is proved that, in a finite group G whose socle is isomorphic to Ln(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(Ln(2)); in this case, A and B are 2-subgroups. All ordered pairs (A,B) of such subgroups are described.
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