On groups generated by three-dimensional special unitary groups I

Abstract

This paper is the result of our attempt to carry over the method of our characterization of the linear groups PSL(n, q) (Phan (1972)) to that of the unitary groups PSU (n, q). It appears desirable to have available a result on the generation of the unitary groups more closely related to the splitting of the underlying hermitian spaces of these groups into orthogonal direct sum of anisotropic lines. Another motivation comes also from our work on the unitary groups in which we obtained a fusion pattern different from that of the unitary group when the dimension of the underlying space is eight. This fusion pattern produces a group whose structure is not immediately apparent. In order to identify this group, the result of this paper appears to be a necessary step.