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arXiv · 1903.05876

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

Chloé Perin
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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 $\mathbb{F}$ must be a free factor. The proof is based on definability of orbits of elements of under automorphisms of $\mathbb{F}$ fixing a large enough subset of $\mathbb{F}$.

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Chloé Perin. 2019-03-14. Elementary subgroups of the free group are free factors - a new proof. https://arxiv.org/abs/1903.05876

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