Root elements and root subgroups in E6(K) for fields K of characteristic two

The purpose of this article is to give an elementary description of the root elements and the root subgroups of the Chevalley group E of type E6(K) in fields K of characteristic two. We show that there is a bijection between the root subgroups of E6 and the family V6 of all 6-dimensional submodules of the 27-dimensional module E6 over K. Then we give a construction of the stabilizer of a 6-dimensional Tits subspace in V6 which is the maximal parabolic subgroup P6 in E6(K).