The generalized Discrete S/sub n/ Method for solution of the multigroup, multidimensional transport equation is investigated. The transport and diffusion equations are derived in difference and differential form based upon a conservation law. The discrete direction representation of the angular integration variable is derived on the basis of a rotationreflection symmetry condition. In addition, if the reason able assumption that the mechanical quadrature point weights are each taken proportional to an area surrounding each point on the unit sphere, then the usual moment conditions are shown valid in an asymptotic sense. In particular, the P/sub n/, DP(sub n/2)-1, and Wick- Chandraseknar methods of solving the transport equation appear now as special cases. The full anisotropic scattering formulation, elementary perturbation theory, and group collapsing techniques are discussed with reference to the proposed equations. The general methods for solving the transport and diffusion difference equations are reviewed briefly. Finally, simple one-dimensional comparisons are made to indicate the treatment of the general method in comparison with other specialized approximation techniques. (auth)