## Olivetti Club

Let $G$ be a group. We say that $G$ is coherent if every finitely generated subgroup of $G$ is finitely presented. One can view coherence as being like a compactness condition. It is known that a covering of a compact surface is another compact surface or a surface with free fundamental group. However, every finitely presented group is the fundamental group of some compact 4-manifold; and yet there are incoherent finitely presented groups. The coherence of groups is a topic of great interest because it is generally more manageable to probe questions about the structure of a group that can be described using a finite amount of data. There has been a lot of work to detect coherence in specific families of groups. A major discovery was that of Peter Scott in his 1973 paper, titled "Finitely generated 3-manifold groups are finitely presented," showing that any finitely generated group that is the fundamental group of a 3-manifold is finitely presented, which is interesting because we do not have a simple classification of the fundamental groups of 3-manifolds.