Exercise 2, § 3

Let X be the set of reductive subalgebras of $\mathfrak{g}$, distinct from $\mathfrak{g}$, and containing $\mathfrak{h}$. Determine the minimal elements of X by means of Chap. VI, §4, Exerc. 4. Show that the centre of such a maximal subalgebra is of dimension 0 or 1, according to whether we are in case a) or case b) of the exercise in question.