Geodesic
Amalgamated Products and the Howson Property
Canadian mathematical bulletin, Tome 40 (1997) no. 3, pp. 330-340

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-1997-039-3
Mots-clés : Primary: 20E06, 20E07, secondary: 20F32 
Kapovich, Ilya. Amalgamated Products and the Howson Property. Canadian mathematical bulletin, Tome 40 (1997) no. 3, pp. 330-340. doi: 10.4153/CMB-1997-039-3
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