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The pro-isomorphic zeta function ζ Γ  ∧ ( s ) of a torsion-free finitely generated nilpotent group Γ enumerates finite index subgroups Δ ≤ Γ such that Δ and Γ have isomorphic profinite completions. It admits an Euler product decomposition ζ Γ  ∧ ( s ) = ∏  p   ζ Γ, p   ∧ ( s )

A nilpotent group without local functional equations for pro-isomorphic subgroups