  For charged semiconductor complexes in magnetic fields B, we discuss an exact
classification of states, which is based on magnetic translations. In this
scheme, in addition to the total orbital angular momentum projection $M_z$ and
electron and hole spins $S_e$, $S_h$, a new exact quantum number appears. This
oscillator quantum number, k, is related physically to the center of the
cyclotron motion of the complex as a whole. In the dipole approximation k is
strictly conserved in magneto-optical transitions. We discuss implications of
this new exact selection rule for internal intraband magneto-optical
transitions of charged excitons $X^-$ in quantum wells in B.
