Subgroup properties of fully residually free groups

Kapovich, Ilya

doi:10.1090/S0002-9947-01-02840-9

Subgroup properties of fully residually free groups
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by Ilya Kapovich

Trans. Amer. Math. Soc. 354 (2002), 335-362

DOI: https://doi.org/10.1090/S0002-9947-01-02840-9

Published electronically: June 27, 2001

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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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