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 language | English (US) |
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Pages (from-to) | 330-340 |
Number of pages | 11 |
Journal | Canadian Mathematical Bulletin |
Volume | 40 |
Issue number | 3 |
DOIs | |
State | Published - Sep 1997 |
Externally published | Yes |
ASJC Scopus subject areas
- General Mathematics