On asymptotic properties of verbal subsets in a group

A. Myasnikov, V. Roman’kov

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that the asymptotic density ρ(w[Fr]) of the verbal set w[Fr] in a free group Fr, r ≥ 2, is equal to 0 for every word w with exponent sum exp(w) ≠ 1. When exp(w) = 1 one has w[Fr] = Fr, and so ρ(w[Fr]) = 1.

Original languageEnglish
Pages (from-to)399-402
Number of pages4
JournalLobachevskii Journal of Mathematics
Volume36
Issue number4
DOIs
StatePublished - 1 Oct 2015

Keywords

  • asymptotic density
  • free group
  • verbal set

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