Finite index subgroups of fully residually free groups

Andrey V. Nikolaev, Denis E. Serbin, O. Kharlampovich

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

Using graph-theoretic techniques for f.g. subgroups of F[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. As an application we obtain an analogue of GreenbergStallings Theorem for f.g. fully residually free groups, and prove that a f.g. nonabelian subgroup of a f.g. fully residually free group is of finite index in its normalizer and commensurator.

Original languageEnglish
Pages (from-to)651-673
Number of pages23
JournalInternational Journal of Algebra and Computation
Volume21
Issue number4
DOIs
StatePublished - Jun 2011

Keywords

  • Fully residually free groups
  • GreenbergStallings Theorem
  • finite index
  • limit groups

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