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Finite index subgroups of fully residually free groups

Andrey Nikolaev, Denis Serbin
Arxiv ID: 0809.0938Last updated: 7/14/2021
Using graph-theoretic techniques for f.g. subgroups of $F^{\mathbb{Z}[t]}$ we provide a criterion for a f.g. subgroup of a f.g. fully residually free group to be of finite index. Moreover, we show that this criterion can be checked effectively. Also we obtain an analogue of Greenberg-Stallings Theorem for f.g. fully residually free groups, and prove that a f.g. non-abelian subgroup of a f.g. fully residually free group is of finite index in its commensurator.

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