Splitting of Normalizers of Maximal Tori in Finite Groups of Lie Type

Let G be a finite group of Lie type, and T some maximal torus of the group G. We bring to a close the study of the question of whether there exists a complement for a torus T in its algebraic normalizer N (G, T). It is proved that any maximal torus of a group G ∈ {G2(q), 2G2(q), 3D4(q)} has a complement in its algebraic normalizer. Also we consider the remaining twisted classical groups 2An(q) and 2Dn(q).