Exercise 1, § 3

Let G be a Lie group and $G_1$ and $G_2$ Lie subgroups of G. Suppose that $G_2$ is of finite codimension in G and that K is of characteristic 0. Then $G_1 \cap G_2$ is a Lie subgroup of G with Lie algebra $L(G_1) \cap L(G_2)$ (argue as in Proposition 29 and its Corollary 2).