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 On the symmetries of the Sol3 Lie group J. Korean Math. Soc.Published online August 23, 2019 Lakehal Belarbi University of Mostaganem Abstract : In this work we consider the $Sol_{3}$ Lie group, equipped with the left-invariant metric, Lorentzian or Riemannian. We determine Killing vector fields and affine vectors fields. Also we obtain a full classification of Ricci, curvature and matter collineations. Keywords : Lorentzian $Sol_{3}$ group, Killing vector fields, Affine vector fields, Ricci collineations, Curvature collineations, matter collineations. MSC numbers : 53C50, 53B30 Full-Text :