The structure of groups having the same elementary theory as free groups is now known: they and their finitely generated subgroups form a prescribed subclass e of the hyperbolic limit groups. We prove that if G 1,...,G n are in e then a subgroup G ? G 1 × ? × G n is of type FP n if and only if G is itself, up to finite index, the direct product of at most n groups from e. This provides a partial answer to a question of Sela. © Birkhäuser Verlag, Basel 2007.
- Bass-Serre theory
- Homological finiteness properties
- Limit groups