  We describe various combinatorial aspects of the Birkhoff-Connes-Kreimer
factorization in perturbative renormalisation. The analog of Bogoliubov's
preparation map on the Lie algebra of Feynman graphs is identified with the
pre-Lie Magnus expansion. Our results apply to any connected filtered Hopf
algebra, based on the pro-nilpotency of the Lie algebra of infinitesimal
characters.
