The Virtual Surjection Conjecture for Discrete Groups
Statement
If a subgroup of a product of groups of type virtually surjects onto every -tuple of factors, must it be of type itself? Yes, for discrete groups, and likewise for . The homological -- Conjecture follows for discrete groups when the common quotient is finitely presented, and that hypothesis cannot be dropped.
Context
A named conjecture on finiteness properties of subgroups of direct products, standard in geometric group theory alongside the n-(n+1)-(n+2) conjecture it implies.
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