Involution widths of skew linear groups generated by involutions

Abstract

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 if s 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.