It is well known that a
closed 3-manifold M contains a (piecewise linearly embedded) essential separating
2-sphere if and only if π1(M) is a nontrivial free product. In this paper necessary
and sufficient conditions, in terms of π1(M), are given for the existence of
a projective plane in M. If M is irreducible this condition is that π1(M)
be an extension of Z or a nontrivial free product by Z2. In particular this
provides a criterion for deciding which irreducible closed 3-manifolds are not
P2-irreducible.