Involution widths of skew linear groups generated by involutions

Let D be a division ring, n an integer greater than 1 and ILn(D) the subgroup of the general linear group GLn(D) generated by all involutions in GLn(D). The aim of this paper is to show that ifs is a natural number such that every element in the commutator group of D* = D\{0} is a product of at most s commutators in D*, then each matrix in ILn(D) is the product of at most 4s + 4 involutions and each matrix in the special linear group SLn(D) is a product of at most 6s + 4 commutators of involutions.(c) 2023 Elsevier Inc. All rights reserved.