On Generation of the Group PGLn(Z + iZ) by Three Involutions, Two of which Commute

The results of the paper relate to the following general problem. Find natural finite generating sets of elements of a given linear group over a finitely generated commutative ring. Of particular interest are coefficient rings that are generated by a single element, for example, the ring of integers or the ring of Gaussian integers. We prove that a projective general linear group of dimension n over the ring of Gaussian integers is generated by three involutions two of which commute if and only if n is greater than 4 and 4 does not divide n. Earlier, M. A. Vsemirnov, R. I. Gvozdev, D. V. Levchuk and the authors of this paper solved a similar problem for the special and projective special linear groups.