Let G=GL(n, q) be a general linear group with a generating set A. Consider G as a finite group with a generating set A. We define the (symmetric) diameter of G with respect to A as the maximum length of the shortest word in ( A ∪A−1)A expressing g, where g ranges over all elements in G. The (symmetric) diameter of G is then the maximum (symmetric) diameter over all possible generat ing sets of G. We use Gn to denote the n-th direct power of G.
