Suppose that L=L(X) is the free Lie p-algebra of finite rank k with free generating set X={x1,…,xk} on a field of positive characteristic. Let G is nontrivial finite group of homogeneous automorphisms L(X). Our main purpose to prove that LG subalgebra of invariants is is infinitely generated. We have more strongly result. Let Y=∪∞n=1Yn be homogeneous free generating set for the algebra of invariants LG, elements Yn are of degree n relatively X, n≥1. Consider the corresponding generating function H(Y,t)=∑∞n=1|Yn|tn.
