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GAFA Geometric And Functional Analysis

, Volume 17, Issue 2, pp 385–403 | Cite as

Subgroups Of Direct Products Of Elementarily Free Groups

  • Martin R. Bridson
  • James Howie
Article

Abstract.

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 \({\mathcal{E}}\) of the hyperbolic limit groups. We prove that if G1,...,G n are in \({\mathcal{E}}\) then a subgroup Γ ⊂ G1 × … × G n is of type FP n if and only if Γ is itself, up to finite index, the direct product of at most n groups from \({\mathcal{E}}\) . This provides a partial answer to a question of Sela.

Keywords and phrases:

Limit groups homological finiteness properties Bass–Serre theory 

AMS Mathematics Subject Classification:

20F65 20E08 20F67 

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Copyright information

© Birkhäuser Verlag, Basel 2007

Authors and Affiliations

  1. 1.Department of MathematicsImperial CollegeLondonUK
  2. 2.Maxwell Institute of Mathematical SciencesHeriot–Watt UniversityEdinburghScotland

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