Amalgamated products and the Howson property

Ilya Kapovich

Research output: Contribution to journalArticlepeer-review

Abstract

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 *U B, 〈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.

Original languageEnglish (US)
Pages (from-to)330-340
Number of pages11
JournalCanadian Mathematical Bulletin
Volume40
Issue number3
DOIs
StatePublished - Sep 1997
Externally publishedYes

ASJC Scopus subject areas

  • General Mathematics

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