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We demonstrate experimentally that a one-dimensional array of silicon nanowires periodically placed on a nickel substrate enhances the transverse magneto-optical Kerr effect (TMOKE) compared to a nickel film. The enhancement mechanism is associated with the excitation of two types of resonances: multipole Mie resonances in each nanowire and surface lattice resonances (SLRs) emerging from the periodic arrangement of the nanowires. The maximal TMOKE values reached up to 1.9 and 2.6% due to the excitation of SLR and a magnetic dipole resonance, respectively. When the SLR is excited, the spectral width of the TMOKE enhancement is narrower compared to the case of the magnetic dipole resonance. [ABSTRACT FROM AUTHOR]