  We attach to any linear endomorphism f of any vector space V a structure of
prelie algebra on the shuffle algebra T(V); we describe its enveloping algebra,
the dual Hopf algebra and the associated group of characters. For f=Id\_V, we
find the algebra of formal diffeomorphisms, seen as a subalgebra of the
Connes-Kreimer Hopf algebra of rooted trees in the context of QFT; for other
well-chosen f, we obtain the groups of Fliess operators in Control Theory. An
algebraic structures of these Com-Prelie Hopf algebras is carried out:
gradations, group of automorphisms, subobject generated by V, etc.
