Wise's incoherence conjecture for free-by-free groups

Let G=FmFnG=F_m\rtimes F_n be a semidirect product of free groups, where m,n2m,n\geq 2. A group is incoherent if it has a finitely generated subgroup that is not finitely presented. Wise's incoherence conjecture. The group GG is incoherent. This conjecture is motivated by the paper's results proving incoherence for broad classes of free-by-free groups, including groups satisfying the excessive-homology criterion; the general case remains open.

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Primary source

Robert Kropholler and Genevieve Walsh, “Incoherence and fibering of many free-by-free groups”, arXiv:1910.09601 (2020).

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