TITLE: Stallings fibration theorem
QUESTION [6 upvotes]: Stallings' fibration theorem states that if we have a compact irreducible $3$-manifold $M^3,$ with 
$G\rightarrow \pi_1(M^3) \rightarrow \mathbb{Z},$ and $G$ is finitely generated and is not of order $2,$ then $M^3$ fibers over a circle. The question is whether the last condition (that $G\neq \mathbb{Z}/2\mathbb{Z}$) is actually necessary (the answer is probably in Stallings' original paper, but I can't find it online).

REPLY [7 votes]: This should follow from geometrization.  The fundamental group of the manifold is $\mathbb{Z}/2\mathbb{Z} \oplus \mathbb{Z}$, and geometrization should tell you that the manifold is then $\mathrm{RP}^2 \times S^1$.
I looked in Stallings's paper, and he says that it is a hard open problem, so this might be the only way.