  Central extensions of the three-dimensional translation group T=Z^3 by the
unitary group U(1) (a group of factors) are considered within the frame of the
Mac~Lane method. All nonzero vectors t in T are considered to be generators of
T. This choice leads to very illustrative relations between the Mac~Lane method
and Zak's approach to magnetic translation groups. It is shown that factor
systems introduced by Zak and Brown can be realized only for the unitary group
U(1) and for some of its finite subgroups.
