Matrix Generators for the Orthogonal Groups

In 1962 Steinberg gave pairs of generators for all finite simple groups of Lie type. In this paper, for each finite orthogonal group we provide a pair of matrices which generate its derived group: the matrices correspond to Steinbergʹs generators modulo the centre. These generators have been implemented in the computer algebra system MAGMA and this completes the provision of pairs of generators in MAGMA for all (perfect) finite classical groups.