GAFA Geometric And Functional Analysis

, Volume 17, Issue 2, pp 385–403

Subgroups Of Direct Products Of Elementarily Free Groups

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,...,Gn are in \({\mathcal{E}}\) then a subgroup Γ ⊂ G1 × … × Gn is of type FPn 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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