  We study an analogue of the notion of p-restricted Lie-algebra and of the
notion of divided power algebra for PreLie-algebras. We deduce our definitions
from the general theory of operads. We consider two variants \Lambda(P,-) and
\Gamma(P,-) of the monad S(P,-) which governs the category of algebras
classically associated to an operad P. For the operad of PreLie-algebras
P=PreLie, we prove that the category of algebras over the monad
\Lambda(PreLie,-) is identified with an already defined category of
p-restricted PreLie-algebras introduced by A. Dzhumadil'daev. We give an
explicit description of the structure an algebra over the monad \Gamma
(PreLie,-) in terms of brace-type operations and we compute the relations
between these generating operations. We prove that classical examples of
PreLie-algebras occurring in deformation theory actually form \Gamma
(PreLie,-)-algebras.
