Finite index subgroups of fully residually free groups

Details Finite index subgroups of fully residually free groups Finite index subgroups of fully residually free groups

2008-09-05

arxiv.org/abs/0809.0938v1

Mathematics

Group Theory

21 pages, 1 figure

Scientific paper

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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