  We show that for closed finite sized systems with an odd number of real
fermionic modes, even in the presence of interactions, there are always at
least two fermionic operators that commute with the Hamiltonian.There is a zero
mode corresponding to the fermion parity operator, as shown by Akhmerov, as
well as additional linearly independent zero modes, one of which is 1) the one
that is continuously connected to the Majorana mode solution in the
non-interacting limit, and 2) less prone to decoherence when the system is
opened to contact with an infinite bath. We also show that in the idealized
situation where there are two or more well separated zero modes each associated
with a finite number of fermions at a localized vortex, these modes have
non-Abelian Ising statistics under braiding. Furthermore the algebra of the
zero mode operators makes them useful for fermionic quantum computation.
