Higher dimensional algebraic fiberings for pro-p groups

2022/05/16 by Dessislava H. Kochloukova, Kochloukova, Dessislava H. · 1 citation
Mathematics · #Finite Group Theory Research #Geometric and Algebraic Topology #Advanced Topology and Set Theory

paper · pdf · doi:10.48550/arxiv.2205.07418

Abstract

We prove some conditions for higher dimensional algebraic fibering of pro-p group extensions and we establish corollaries about incoherence of pro-p groups. In particular, if G = K \rtimes Γ is a pro-p group, Γ a finitely generated free pro-p group with d(Γ) ≥ 2, K a finitely presented pro-p group with N a normal pro-p subgroup of K such that K/ N ≃ ℤ_p and N not finitely generated as a pro-p group, then G is incoherent (in the category of pro-p groups). Furthermore we show that if K is a free pro-p group with d(K) = 2 then either Aut₀(K) is incoherent (in the category of pro-p groups) or there is a finitely presented pro-p group, without non-procyclic free pro-p subgroups, that has a metabelian pro-p quotient that is not finitely presented i.e. a pro-p version of a result of Bieri-Strebel does not hold.

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• Toric arrangements and Bloch-Kato pro-p groups

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