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Amalgamated Products and the Howson Property

Published online by Cambridge University Press:  20 November 2018

Ilya Kapovich*
Affiliation:
Department of Mathematics, City College of the City University of New York, Convent Avenue at 138-th Street, New York, New York 10031 U.S.A., e-mail ilya@groups.sci.ccny.cuny.edu
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Abstract

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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.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1997

References

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