Exercise 5, § 6

In the notation of Exercise 9 of § 1, show that $H'$ is an integral subgroup of $H$. Deduce that in the simply connected group $\mathbf{SU}(2, \mathbf{C}) \times \mathbf{SU}(2, \mathbf{C})$ (§ 3, Exercise 7 (c)), there exist one-parameter subgroups which are not closed.