  We classify solvable Lie groups with a free nilradical admitting an Einstein
left-invariant metric. Any such group is essentially determined by the
nilradical of its Lie algebra, which is then called an Einstein nilradical. We
show that among the free Lie algebras, there are very few Einstein nilradicals.
Except for the one-step (abelian) and the two-step ones, there are only six
others: f(2,3), f(2,4), f(2,5), f(3,3), f(4,3), f(5,3) (where f(m,p) is a free
p-step Lie algebra on m generators). The reason for that is the inequality-type
restrictions on the eigenvalue type of an Einstein nilradical obtained in the
paper.
