so that's definitely a possible fundamental group of a manifold but if you consider all the other conditions of the fibering conjecture it's not allowed h infinite means there's a non separating surface irrreduciblity means it can't be a sphere compressing the surface gives a pi injective surface so the manifold group contains a surface subgroup which can't be the case if it's the integers since the sphere is excluded actually the conclusion that the manifold fibers implies that the group contains a surface subgroup the surface can't be a sphere because of irreducibility so we have a more complicated surface whose fundamental group injects into the fundamental group of the manifold