Submission date: 14 March 2019

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 must be a free factor. The proof is based on definability of orbits of elements of under automorphisms of 𝔽 fixing a large enough subset of 𝔽.

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Full text arXiv 1903.05876: pdf, ps.