  The Bogoliubov model for weakly interacting Bose gas is extended to
Bose-Einstein condensation (BEC) of spin-S atoms in a magnetic field. Equation
for the vectorial order parameter valid at temperature $T\to 0$ is derived and
its particular solution is found. This solution corresponds to the formation of
BEC of atoms with a definite spin projection onto direction of a magnetic
field. We study the thermodynamic stability of the found solution and obtain
the expressions for low-lying collective modes.
