# A note on morphisms to wreath products

@inproceedings{Genevois2021ANO, title={A note on morphisms to wreath products}, author={Anthony Genevois and Romain Tessera}, year={2021} }

Given a morphism φ : G → AoB from a finitely presented group G to a wreath product A o B, we show that, if the image of φ is a sufficiently large subgroup, then ker(φ) contains a non-abelian free subgroup and φ factors through an acylindrically hyperbolic quotient of G. As direct applications, we classify the finitely presented subgroups in A o B up to isomorphism and we deduce that a group having a wreath product (non-trivial) o (infinite) as a quotient must be SQ-universal (extending theorems…

## One Citation

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