GAFA Geometric And Functional Analysis

, Volume 17, Issue 2, pp 385–403

Subgroups Of Direct Products Of Elementarily Free Groups


DOI: 10.1007/s00039-007-0600-4

Cite this article as:
Bridson, M.R. & Howie, J. GAFA, Geom. funct. anal. (2007) 17: 385. doi:10.1007/s00039-007-0600-4


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 

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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