A note on the action of the primitive Milnor operations on the Dickson invariants

In this note, we present a formula for the action of the primitive Milnor operations on generators of algebra of invariants of the general linear group $GL_n=GL(n, \mathbb F_p)$ in the polynomial algebra $P_n= \mathbb F_p[x_1,x_2,\ldots,x_n]$ with $p$ an odd prime number.