On endomorphisms of free groups that preserve primitivity

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It is proven that if φ is an endomorphism of a free group Fn = <X1, ⋯, Xn> of rank n such that φ(u) is primitive whenever so is u ∈ Fn and φ(Fn) contains a primitive pair (i.e., a pair α(x1), α(x2) with α ∈ Aut fn), then φ is an automorphism. Also, every endomorphism of F2 that preserves primitivity is an automorphism.

Original languageEnglish (US)
Pages (from-to)92-100
Number of pages9
JournalArchiv der Mathematik
Issue number2
StatePublished - Feb 3 1999

ASJC Scopus subject areas

  • General Mathematics


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