Normal, unipotent subgroup schemes of reductive groups

Abstract

Let G be a reductive group over a field k of characteristic p. Let k sep be a separable closure of k. If p ≠ 2 , there exists a linear representation of G that is faithful and semisimple; moreover, any unipotent, normal subgroup scheme of G is trivial. For p = 2 , these two properties hold if and only if G k sep has no direct factor that is isomorphic to SO 2 n + 1 for some n ⩾ 1 . To cite this article: A. Vasiu, C. R. Acad. Sci. Paris, Ser. I 341 (2005).