  We study a swimming undulating sheet in the isotropic phase of an active
nematic liquid crystal. Activity changes the effective shear viscosity,
reducing it to zero at a critical value of activity. Expanding in the sheet
amplitude, we find that the correction to the swimming speed due to activity is
inversely proportional to the effective shear viscosity. Our perturbative
calculation becomes invalid near the critical value of activity; using
numerical methods to probe this regime, we find that activity enhances the
swimming speed by an order of magnitude compared to the passive case.
