  This work shows that a strongly correlated phase which is gapped to
collective spin excitations but gapless to charge fluctuations emerges as a
universal feature in one-dimensional fermionic systems obeying certain
symmetries. Namely, nanowires interacting via Coulomb repulsion which are
symmetric under time-reversal and spatial inversion symmetry exhibit spin gaps
whenever one pair of spin-degenerate subbands is occupied and an arbitrarily
weak spin-orbit interaction is present. This general result is independent of
the details of the one-dimensional confinement, the fermionic spin or nature of
the spin-orbit interaction. In narrow-gap semiconductors, this gap may be of
order 10 \textmu eV. This strongly correlated phase may be identified both via
an anomalous $h/2e$ flux periodicity in Aharonov-Bohm oscillations and $2e$
periodic Coulomb blockade, features which reflect the existence of fermionic
pairing despite the absence of superconductivity and the repulsive nature of
the interaction.
