Two-Element Generation of Unitary Groups Over Finite Fields

摘要

Let V be a nonsingular A-hermitian space of dimension n over a field K and U(V) the unitary group on V. Under the assumption that K is a finite field of characteristic different from 2 and V is isotropic, Ishibashi showed in 12 that U(V) is generated by three elements. Further, in fact, he proved that when the unitary group U(V) is the symplectic group Sp(V), then U(V) is generated by just two elements. Minimal sets of generators of the unitary groups of nonsingular A-hermitian spaces over a finite field of odd characteristic are studied. All such unitary groups are shown to be generated by two elements.