Geodesic
On invariants of modular free Lie algebras
Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 117-124

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Suppose that $L(X)$ is a free Lie algebra of finite rank over a field of positive characteristic. Let $G$ be a nontrivial finite group of homogeneous automorphisms of $L(X)$. It is known that the subalgebra of invariants $H=L^G$ is infinitely generated. Our goal is to describe how big its free generating set is. Let $Y=\bigcup_{n=1}^\infty Y_n$ be a homogeneous free generating set of $H$, where elements of $Y_n$ are of degree $n$ with respect to $X$. We describe the growth of the generating function of $Y$ and prove that $|Y_n|$ grow exponentially. 
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     author = {V. M. Petrogradsky and A. A. Smirnov},
     title = {On invariants of modular free {Lie} algebras},
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     publisher = {mathdoc},
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     number = {1},
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a7/}
}
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V. M. Petrogradsky; A. A. Smirnov. On invariants of modular free Lie algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 15 (2009) no. 1, pp. 117-124. http://geodesic.mathdoc.fr/item/FPM_2009_15_1_a7/