  Three-wave interactions of plasma waves propagating parallel to the mean
magnetic field at frequencies below the electron cyclotron frequency are
considered. We consider Alfv\'en--ion-cyclotron waves,
fast-magnetosonic--whistler waves, and ion-sound waves. Especially the weakly
turbulent low-beta plasmas like the solar corona are studied, using the
cold-plasma dispersion relation for the transverse waves and the
fluid-description of the warm plasma for the longitudinal waves. We analyse the
resonance conditions for the wave frequencies $\omega$ and wavenumbers $k$, and
the interaction rates of the waves for all possible combinations of the three
wave modes, and list those reactions that are not forbidden.
