An analysis is reported on the channel e(+)e(-) --> mu(+)mu(-)(n gamma), n=1,2.., using data taken with the DELPHI detector at LEP from 1990 to 1992. Differential cross sections of the radiative photons as a function of photon energy and of the angle between the photon and the muon are presented. No significant deviations from expectations are observed. The data are also used to extract the muon-pair cross section and asymmetry below the Z(0) peak by using those events with relatively hard initial state radiative photon(s). The measured cross section and asymmetry show no significant deviation from the Standard Model expectations. These results together with the DELPHI cross section and asymmetry measurements at the LEP energies from the 1990 to 1992 running periods are used to determine limits on the Z(0)-Z' gauge boson mixing angle theta(Z') and on the Z' mass. There is no indication of the existence of a Z'; the limits obtained on the mixing angle substantially improve upon existing limits. The 95% confidence level allowed ranges of theta(Z') in various models are: -0.0070 less than or equal to theta(Z') less than or equal to 0.0078, E(6)(chi) model, -0.0075 less than or equal to theta(Z') E(6)(psi) model, -0.029 less than or equal to theta(Z') less than or equal to 0.029, E(6)(eta) model, -0.0068 less than or equal to theta(Z') less than or equal to 0.0082, L-R(1.) model, -0.0057 less than or equal to theta(Z') less than or equal to 0.0077, L-R(root 2) model.
