Symmetry of the order parameter in the UGe$_2$

For the UGe$_2$ ferromagnetic superconductor, the forms of the order parameter are determined with allowance for the crystal symmetry and with the assumption that a strong spin-orbit interaction is present in the system. The limiting case corresponding to the immediate vicinity of the simultaneous transition to the superconducting and ferromagnetic phases is considered. The opposite limit corresponding to a wide separation of the Fermi surfaces with opposite spin orientations is considered as well. Possible effects of the ferromagnetic domain structure on the properties of UGe$_2$ in the superconducting state are discussed.