• Corpus ID: 239024431

A note on morphisms to wreath products

  title={A note on morphisms to wreath products},
  author={Anthony Genevois and Romain Tessera},
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… 
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