Exercise 3, § 4

a) Show that the automorphism $\sigma : A \rightarrow \overline{A}$ of $\mathbf{S}\mathbf{U}(n,\mathbf{C})$ is not inner for $n\geq 3$. Every non-inner automorphism of $\mathbf{S}\mathbf{U}(n,\mathbf{C})$ is of the form (Int $g$)$\circ \sigma$, $g\in \mathbf{S}\mathbf{U}(n,\mathbf{C})$.

b) Show that for every almost simple connected compact group G of type $A_n$ $(n\geq 2)$, the group Aut(G)$/$Int(G) is cyclic of order 2 (cf. §3, Exerc. 4).