GAFA Geometric And Functional Analysis

, Volume 17, Issue 2, pp 385–403

Subgroups Of Direct Products Of Elementarily Free Groups


    • Department of MathematicsImperial College
  • James Howie
    • Maxwell Institute of Mathematical SciencesHeriot–Watt University

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 G 1,...,G n are in \({\mathcal{E}}\) then a subgroup Γ ⊂ G 1 × … × 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

Copyright information

© Birkhäuser Verlag, Basel 2007