On Rationality of Verbal Subsets in a Group

A. Myasnikov, V. Roman'kov

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Let F be a free non-abelian group. We show that for any group word w the set w[F] of all values of w in F is rational in F if and only if w[F]=1 or w[F]=F. We generalize this to a wide class of free products of groups.

Original languageEnglish
Pages (from-to)587-598
Number of pages12
JournalMathematical Systems Theory
Volume52
Issue number4
DOIs
StatePublished - May 2013

Keywords

  • Finite automata
  • Free groups
  • Free products
  • Verbal sets

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