On Certain Elements of Free Groups

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LetFmbe a free group of finite rankm. It is proven that for everyn≥2 there is a non-trivial wordwn(x1,...,xn) such that if valueswn(Un),wn(Vn) ofwn(x1,...,xn) on twon-tuplesUnandVnof elements ofFmare conjugate and non-trivial then thesen-tuples themselves are conjugate. As a corollary, one has the existence of two elements inFmwhose images uniquely determine any monomorphism ψ:Fm→Fm.

Original languageEnglish (US)
Pages (from-to)394-405
Number of pages12
JournalJournal of Algebra
Issue number2
StatePublished - Jun 15 1998

ASJC Scopus subject areas

  • Algebra and Number Theory


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