Symmetry Coefficients of Semilinear Partial Differential Equations

We show that for any semilinear partial differential equation of order $m$, the infinitesi-mals of the independent variables depend only on independent variables and, if $m>1$ and the equation also is linear in derivatives of order $m-1$ of the dependent variable, then the infinitesimal of the dependent variable at most is linear on it. Many examples of important partial differential equations in Analysis, Geometry and Mathematical - Physics are given in order to enlighten the main result.