Abstract
About Generating Set of the Invariant Subalgebra of Free Restricted Lie Algebra V. M. Petrogradsky, I. A. Subbotin Department of Mathematics, University of Brasilia, 70910-900 Brasilia DF, Brazil, petrogradsky@rambler.ru Ulyanovsk State University, Russia, 432970, Ulyanovsk, ul. L’va Tolstogo, 42, shelby888@yandex.ru Suppose thatL = L(X) is the free Lie p–algebra of finite rank k with free generating setX = {x1, . . . , xk} on a field of positive characteristic. LetG is nontrivial finite group of homogeneous automorphismsL(X). Our main purpose to prove thatL 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 L, elements Yn are of degree n relatively X , n ≥ 1. Consider the corresponding generating function H (Y, t) = ∞
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