  The process of neutrino propagation through an active medium consisting of
magnetic field and plasma is analysed. We consider in detail the contribution
of a magnetic field B into the neutrino self-energy operator Sigma (p). The
results for this contribution were contradictory in the previous literature.
For the conditions of the early universe where the background medium consists
of a charge-symmetric plasma, the pure B-field contribution to the neutrino
dispersion relation is proportional to (e B)^2 and thus comparable to the
contribution of the magnetized plasma. The neutrino self-energy operator Sigma
(p) is calculated also for the case of high-energy neutrinos, which corresponds
to the crossed field approximation. The probability of the neutrino decay nu to
e^- W^+ is calculated from the imaginary part of the Sigma (p) operator. A
simple analytical result is obtained for the most interesting region of
parameters which was not considered earlier. The external magnetic field
contribution into the neutrino magnetic moment is calculated. The result
obtained corrects the formulas existed earlier. We show qualitatively that the
effect of ``neutrino spin light'' discussed in the literature has no physical
region of realization because of the medium influence on photon dispersion.
