Exercise 8, § 3

Let G be an almost simple, connected, compact Lie group of type $A_n,B_n,C_n,D_n$ or $G_2$. Prove that $\pi_2(G) = 0$ and $\pi_3(G) =\mathbf{Z}$ (use Exerc. 2 to 7 and the fact that $\pi_i(\mathbf{S}_n)$ is zero for $i < n$ and cyclic for $i=n$ (cf. General Topology, Chap. XI).