Products of unipotent matrices of index 2 over division rings (Q6607757)

In this paper the authors consider products of unipotent matrices of index 2 over a division ring that need not be of finite degree but of infinite degree also. Here the finite and infinte matrices are understood matrices of finite and infinte degree. First the unipotent matrices of index 2 are given in several cases and then the subgroups generated by such matrices are investgated. Finally, the authors give estimate for the unipotency length of matrices in these subgroups, that is, they estimate a positive integer \(d\) such that these matrices can be written as a product of at most \(d\) unipotent matrices of index 2. The matrix decomposition in GL2(\(D\)) is investigated in more details.