English

Elementary subgroups of the free group are free factors - a new proof

Logic 2019-03-15 v1 Group Theory

Abstract

In this note we give a new proof of the fact that an elementary subgroup (in the sense of first-order theory) of a non abelian free group F\mathbb{F} must be a free factor. The proof is based on definability of orbits of elements of under automorphisms of F\mathbb{F} fixing a large enough subset of F\mathbb{F}.

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Cite

@article{arxiv.1903.05876,
  title  = {Elementary subgroups of the free group are free factors - a new proof},
  author = {Chloé Perin},
  journal= {arXiv preprint arXiv:1903.05876},
  year   = {2019}
}