Abstract: We investigate fixed points of an automorphism of a free solvable Lie algebra which permutes the generators cyclically. Let ? be a cyclic permutation of order n which belongs to the nth symmetric group S_n. We give form of the fixed points of an automorphism of a free solvable Lie algebra which is induced by the permutation ?.

Keywords: Free Solvable Lie algebra, automorphism, fixed point, cyclic permutation.