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
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.
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
@article{10_4153_CMB_1997_039_3,
author = {Kapovich, Ilya},
title = {Amalgamated {Products} and the {Howson} {Property}},
journal = {Canadian mathematical bulletin},
pages = {330--340},
year = {1997},
volume = {40},
number = {3},
doi = {10.4153/CMB-1997-039-3},
url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1997-039-3/}
}
Cité par Sources :