Exercise 1, § 3

Let G be a compact Lie group of dimension $>0$. Then every finite commutative subgroup of G is cyclic if and only if G is isomorphic to $\mathbf{U},\mathbf{S}\mathbf{U}(2,\mathbf{C})$ or the normalizer of a maximal torus in $\mathbf{S}\mathbf{U}(2,\mathbf{C})$.