Minimal length factorizations of finite simple groups of Lie type by unipotent Sylow subgroups

Abstract

We prove that every finite simple group G of Lie type satisfies G = UU−UU − where U is a unipotent Sylow subgroup of G and U − is its opposite. We also characterize the cases for which G = UU−U. These results are best possible in terms of the number of conjugates of U in the above factorizations