Products of Involutions in Steinberg Group over Skew Fields

Abstract Consider the stable Steinberg group St(K) over a skew field K. An element x is called an involution if x ² = 1. In this paper, an involution is allowed to be the identity. The authors prove that an element A of GL _n (K) up to conjugation can be represented as BC, where B is lower triangular and C is simultaneously upper triangular. Furthermore, B and C can be chosen so that the elements in the main diagonal of B are β ₁, β ₂,⋯ , β _n , and of C are γ ₁, γ ₂, ⋯, γ _n c _n , where c _n ∈K*,K*] and It is also proved that every element δ in St(K) is a product of 10 involutions. *Project supported by the Key Project of the Ministry of Education of China (No. 03060).