  Projective irreps of (Z_N)^2 can be labelled by divisors n of N. A product of
two irreps, labelled by n and n', can be decomposed into projective irreps
labelled by M, where M strongly depends on the arithmetic structure of N, n, n'
and their relations (gcd, lcm etc.). Such decompostion describes two important
physical effects: (i) changes of a magnetic period of the crystal lattice (with
unchaged crystal period N); (2) each representation can be related with a
charged particle moving in an external magnetic field and a periodic potential
--- a product of (projective) irreps corresponds to interaction of particles
with charges Q and Q', respectively, and the decomposition corresponds to a
particle with the charg Q''=Q+Q'.
