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Creators/Authors contains: "Kropholler, Robert P"

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  1. ; (, Annales de l'Institut Fourier)
    A group is called free-by-free if it is the semi-direct product of two finitely generated free groups. A group is coherent if any finitely generated subgroup is finitely presented, and incoherent otherwise. In this paper, the authors provide evidence towards the conjecture (due independently to the authors and Dani Wise) that every free-by-free group is incoherent. To do this, they give a homological condition which lets them conclude that the free-by-free group has a finite index subgroup which surjects onto ℤ with finitely generated kernel; standard arguments imply that this kernel cannot be finitely presented. As an important special case, they show that if the free-by-free group is hyperbolic and virtually special, then it is incoherent. 
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