A normal subgroup of a strongly reductive subgroup is strongly reductive (Q1400189)

Let \(G\) be a reductive linear algebraic group over an algebraically closed field \(k\), and \(H\) a strongly reductive subgroup of \(G\). The main result of this paper is to prove that any closed normal subgroup of \(H\) is still strongly reductive. When \(G\) is the general linear group over \(k\), this is a consequence of the Clifford theorem in representation theory.