15.67 (2002)

The groups $\text{SL}_n(\mathbb{Z})$, $n > 13$, satisfy this condition (M. C. Tamburini, P. Zucca, J. Algebra, 195, no. 2 (1997), 650–661). The groups $\text{PSL}_n(\mathbb{Z})$ satisfy it if and only if $n > 4$ (N. Ya. Nuzhin, Vladikavkaz. Mat. Zh., 10, no. 1 (2008), 68–74 (Russian)). The group $\text{PSp}_4(\mathbb{Z})$ does not satisfy it, which follows from the corresponding fact for $\text{PSp}_4(3)$, see 7.30. The group $G_2$ satisfies it (I. A. Timofeenko, J. Siberian Fed. Univ. Ser. Math. Phys., 8, no. 1 (2015), 104–108). The group $E_l$ satisfies it (I. A. Timofeenko, Sibirsk. Èlectron. Mat. Izv., 14 (2017), 807–820 (Russian)).