Subgroups of direct products of elementarily free groups

Martin R. Bridson, James Howie

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)385-403
Number of pages19
JournalGeometric and Functional Analysis
Issue number2
Publication statusPublished - Jun 2007


  • Bass-Serre theory
  • Homological finiteness properties
  • Limit groups


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