Free groups in normal subgroups of the multiplicative group of a division ring

Let D be a division ring with center Z   and multiplicative group D∖{0}=D
• D∖{0}=D
• , and let N   be a normal subgroup of D
• D
• . We investigate various conditions under which N must contain a free noncyclic subgroup. In one instance, assuming that the transcendence degree of Z over its prime field is infinite, and that N contains a nonabelian solvable subgroup, we use a construction method due to Chiba to exhibit free generators of the free subgroup.