  We study Zeeman splitting of zone-center subband edges in a cylindrical hole
wire subject to a magnetic field parallel to its axis. The g-factor turns out
to fluctuate strongly as a function of wire-subband index, assuming values that
differ substantially from those found in higher-dimensional systems. We analyze
the spin properties of hole-wire states using invariants of the spin-3/2
density matrix and find a strong correlation between g-factor value and the
profile of hole-spin polarization density. Our results suggest possibilities
for confinement engineering of hole spin splittings.
