  Results obtained for the antisymmetric gauge A=[Hy,-Hx]/2 by Brown and Zak
are compared with those based on pure group-theoretical considerations and
corresponding to the Landau gauge A=[0,Hx]. Imposing the periodic boundary
conditions one has to be very careful since the first gauge leads to a factor
system which is not normalized. A period N introduced in Brown's and Zak's
papers should be considered as a magnetic one, whereas the crystal period is in
fact 2N. The `normalization' procedure proposed here shows the equivalence of
Brown's, Zak's, and other approaches. It also indicates the importance of the
concept of magnetic cells. Moreover, it is shown that factor systems (of
projective representations and central extensions) are gauge-dependent, whereas
a commutator of two magnetic translations is gauge-independent. This result
indicates that a form of the vector potential (a gauge) is also important in
physical investigations.
