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Preprint Number 1703

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1703. Simon André (IRMAR)
Elementary subgroups of virtually free groups

Submission date: 13 December 2019


We give a description of elementary subgroups (in the sense of first-order logic) of finitely generated virtually free groups. In particular, we recover the fact that elementary subgroups of finitely generated free groups are free factors. Moreover, we give an algorithm that takes as input a finite presentation of a virtually free group G and a finite subset X of G, and decides if the subgroup of G generated by X is ∃∀∃-elementary. We also prove that every elementary embedding of an equationally noetherian group into itself is an automorphism.

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Full text arXiv 1912.06388: pdf, ps.

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