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The complex permeability of an iron-oxide nanosuspension has been measured as a function of magnetic field strength at RF and microwave frequencies using a loop-gap resonator. The particles were suspended in water and had an 8-nm diameter Fe$_3$O$_4$ core that was coated by Dextran. The real part of the permeability increased sharply beyond a frequency-dependent threshold value of the static magnetic field before saturating. Just beyond this threshold field, there was a peak in the imaginary part of the permeability. The permeability measurements, which exhibited features associated with ferromagnetic resonance, were used to determine the dependence of the microwave absorption on static magnetic field strength. Using the absorption data, the $g$-factor of the nanosuspension was found to be $1.86\pm 0.07$., Comment: 7 pages, 6 figures