  We construct an associative product on the symmetric module S(L) of any
pre-Lie algebra L. Then we proove that in the case of rooted trees our
construction is dual to that of Connes and Kreimer. We also show that symmetric
brace algebras and pre-Lie algebras are the same. Finally, using brace algebras
instead of pre-Lie algebras, we give a similar interpretation of Foissy's Hopf
algebra of planar rooted trees.
