Abstract
Let D be a division ring with center Z and multiplicative group D∖{0}=D•, and let N be a normal subgroup of 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.
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