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1 results

  • Amalgamated Products and the Howson Property

  • Ilya Kapovich
  • Journal:
    Canadian Mathematical Bulletin / Volume 40 / Issue 3 / 01 September 1997
    Published online by Cambridge University Press:
    20 November 2018, pp. 330-340
    Print publication:
    01 September 1997
    • Article
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  • We show that if A is a torsion-free word hyperbolic group which belongs to class (Q), that is all finitely generated subgroups of A are quasiconvex in A, then any maximal cyclic subgroup U of A is a Burns subgroup of A. This, in particular, implies that if B is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated) then A *UB, ⧼A, t | Ut = V⧽ are also Howson groups. Finitely generated free groups, fundamental groups of closed hyperbolic surfaces and some interesting 3-manifold groups are known to belong to class (Q) and our theorem applies to them. We also describe a large class of word hyperbolic groups which are not Howson.