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Subgroup properties of fully residually free groups


Author: Ilya Kapovich
Journal: Trans. Amer. Math. Soc. 354 (2002), 335-362
MSC (2000): Primary 20F65
DOI: https://doi.org/10.1090/S0002-9947-01-02840-9
Published electronically: June 27, 2001
MathSciNet review: 1859278
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Abstract:

We prove that fully residually free groups have the Howson property, that is the intersection of any two finitely generated subgroups in such a group is again finitely generated. We also establish some commensurability properties for finitely generated fully residually free groups which are similar to those of free groups. Finally we prove that for a finitely generated fully residually free group the membership problem is solvable with respect to any finitely generated subgroup.


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Additional Information

Ilya Kapovich
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 West Green Street, Urbana, Illinois 61801
Email: kapovich@math.uiuc.edu

DOI: https://doi.org/10.1090/S0002-9947-01-02840-9
Received by editor(s): August 26, 1999
Received by editor(s) in revised form: February 8, 2001
Published electronically: June 27, 2001
Article copyright: © Copyright 2001 American Mathematical Society

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