  We study the effects of Majorana modes and interactions between electrons on
transport in a one-dimensional system with a junction of three p-wave
superconductors (SCs) which are connected to normal metal leads. For
sufficiently long SCs, there are zero energy Majorana modes at the junctions
between the SCs and the leads,and, depending on the signs of the p-wave
pairings in the three SCs, there can also be one or three Majorana modes at the
junction of the three SCs. We show that the various sub-gap conductances have
peaks occurring at the energies of all these modes; we therefore get a rich
pattern of conductance peaks. Next, we use a renormalization group approach to
study the scattering matrix of the system at energies far from the SC gap. The
fixed points of the renormalization group flows and their stabilities are
studied; we find that the scattering matrix at the stable fixed point is highly
symmetric even when the microscopic scattering matrix and the interaction
strengths are not symmetric. We discuss the implications of this for the
conductances. Finally we propose an experimental realization of this system
which can produce different signs of the p-wave pairings in the different SCs.
