Exercise 5, § 9

Let G be a finite-dimensional connected real or complex Lie group. Let $(G_0, G_1, \ldots)$ be the upper central series of G (Chapter II, § 4, Exercise 18) and let $(\mathfrak{g}_0, \mathfrak{g}_1, \ldots)$ be the upper central series of the Lie algebra $L(G)$ (Chapter I, § 1, no. 6). Then, for all $i$, $G_i$ is a Lie subgroup of G such that $L(G_i) = \mathfrak{g}_i$.