  Let k be an algebraically closed field of positive characteristic and G a
simple algebraic group defined over k. Under the assumption that the
characteristic is a good prime for G, we determine a maximal G-stable
subvariety U' of the variety of unipotent elements of G such that for all u in
U' any two A1-subgroups of G containing u are G-conjugate. This result
establishes to what degree an analogue of the Jacobson-Morozov theorem for Lie
algebras is valid for simple algebraic groups defined over fields of (good)
positive characteristic
