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The Virtual Surjection Conjecture for Discrete Groups

Algebra · posed by Martin Bridson, James Howie, Charles Miller III, Hamish Short, 2013 · solved

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Statement

If a subgroup of a product of groups of type FkF_k virtually surjects onto every kk-tuple of factors, must it be of type FkF_k itself? Yes, for discrete groups, and likewise for FPkFP_k. The homological nn-(n+1)(n+1)-(n+2)(n+2) Conjecture follows for discrete groups when the common quotient is finitely presented, and that hypothesis cannot be dropped.

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No person has examined this. Nothing here has been checked at all. say whether it holds →

  1. proof attempt · #1

    Tal Cohen and Mark Shusterman, using GPT

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