Various subgroups of Aut(Cn)${\rm{Aut}}({\mathbb{C}}^{n})$

In this paper, using ideas of Andersén and Lempert on the group of holomorphic automorphisms Aut(Cn)${\rm{Aut}}({\mathbb{C}}^{n})$ ( n⩾2$n\geqslant 2$ ), we prove that the subgroups in Aut(Cn)${\rm{Aut}}({\mathbb{C}}^{n})$ and Autsp(C2n)${\rm{Aut}}_{\rm{sp}}({\mathbb{C}}^{2n})$ ( n⩾2$n\geqslant 2$ ) generated by different types of ‘shears’ are all distinct, which answer affirmatively to two conjectures posed by Forstnerič.