Malnormal subgroups of free groups

A subgroup H of a group G is malnormal if for any g ∈ G, g ∈ H, then g^-1Hg ∩ H = {1}. Here we give a complete characterization of rank 2 malnormal subgroups of free groups. In particular a 2-generator subgroup of a free group F is malnormal if and only if it is isolated and malnormal on generators. The result is not true for greater rank subgroups. This theorem was motivated by a recent algorithm developed by Baumslag, Myasnikov and Remeslennikov that decides whether a subgroup of a free group is malnormal or not.