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We report experimental results on magnetic properties of our fabricated nickel nanodot arrays studied with magnetic force microscopy (MFM) and magneto-optical Kerr effect (MOKE). Arrays of nickel dots with different size and periodicity were fabricated by electron-beam (E-B) lithography and lift-off processes. 50 nm thick arrays (200 nm$,times,$ 200 nm) of nickel dots exhibit that the magnetization occurs independently in terms of the direction of applied field, while smaller arrays (120 nm$,times,$80 nm) with thicknesses ranging from 12 nm to 35 nm show the effect of size and configuration of arrays whose magnetic responses are different. Thinner dots in such array seem to assume single domain state with a preferential easy and hard axis in the array, but thicker dots show a vortex type remanent magnetization. We ascribe the existence of the preferential magnetization axis to a dipolar-dipolar interaction due to small separation of single domain dots.