Composition series for unipotent group varieties (Q1089056)

Let U be a unipotent group variety over an arbitrary field k. Let \(T\times U\to U\) be an action by group automorphisms of a torus T on U. Everything is defined over k. The author proves (in a very short way) the following theorem: If the action of T on the Lie algebra of U is diagonalizable over k, we have a T-invariant composition series defined over k for U with one-dimensional factors.