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We investigate reentrant superconductivity in an Ising ferromagneticsuperconductor URhGe under a transverse magnetic field h_x. The superconductingtransition temperature for p-wave order parameters T_{sc} is calculated andshows two domes as a function of h_x. We find strong enhancement of T_{sc} inthe high-field dome near a saturation field h_s where the spins align in thetransverse direction. Soft magnons generate strong attractive interactionsthere. Spin components of the pairing show a significant change between h_x<h_sand h_x>h_s. We also discuss the appearance of superconductivity with zero-spinpair due to cancellation between external and exchange fields.

p-wave superconductivity near a transverse saturation field