Certain Simple Maximal Subfields in Division Rings

Let D be a division ring finite dimensional over its center F. The goal of this paper is to prove that for any positive integer n there exists a ∈ D⁽ⁿ⁾, the n-th multiplicative derived subgroup, such that F(a) is a maximal subfield of D. We also show the statement holds valid if we replace D⁽ⁿ⁾ with D_n, the n-th additive derived subgroup in case D is of characteristic zero.