Symmetries and reductions of nonlinear Schrِdinger equations of Doebner-Goldin type

We compute symmetry algebras for nonlinear Schrِdinger equations which contain an imaginary nonlinearity as derived by Doebner and Goldin and certain real nonlinearities not depending on the derivatives. In the three-dimensional case we find the maximal symmetry algebras for equations of this type. Admitting other imaginary nonlinearities does lead to similar symmetry algebras. These symmetries are used to obtain explicit solutions of these equations by means of reduction.