Commutators in special linear groups over certain division rings - Bien, M. H.; Lam, P. L. P.; Mai, V. T. (Ukrains’kyi Matematychnyi Zhurnal, 2023)
UDC 512.5 We consider the question whether an element of a special linear group SL_m(D) of degree m1 over a division ring D is a commutator. Our first aim is to show that if the division ring D is algebraically closed and finite-dimensional over its center, then every element of SL_m(D) is a commutator of SL_m(D). We also indicate that this question is related to the derived series in division rings and then describe the derived series in the Mal’cev–Neumann division rings of noncyclic free groups over fields.