Covering numbers with involutions in decomposing infinite matrices

Let D be a division ring. The aim of this paper is to explore the problem of decomposing an infinite matrix over D into a product of involutions and a product of commutators of involutions within the context of covering numbers. Specifically, we focus on decomposing matrices in the commutator subgroup SLV K,∞(D) of the Vershik–Kerov group and in the subgroup SL∞(D) of the stable general linear group GL∞(D).