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LYSO scintillation crystals, due to their significant characteristics such as high light yield, fast decay time, small Moli\'ere radius, and good radiation hardness, are proposed to be used for the electromagnetic calorimeter section of the Turkish Accelerator Center Particle Factory (TAC-PF) detector. In this work, the center of gravity technique was used to determine the impact coordinates of an electron initiating an electromagnetic shower in the LYSO array, the calorimeter module contains nine crystals, each 25 mm$\times$25 mm in cross-section and 200 mm in length. The response of the calorimeter module has been studied with electrons having energies in the range 0.1 GeV-2 GeV. By using the Monte Carlo simulation based on Geant4, the two-dimensional position resolution of the module is obtained as $\sigma_{R}(mm)=((3.95\pm0.08)/\sqrt{E})\oplus(1.91\pm0.11)$ at the center of the crystal., Comment: 5 pages, 8 figures