The paper proves that the average number of Γ-equivariant surjections from the maximal unramified split-at-∞ Galois group onto any admissible group H is 1/[H^{Γ∞}:H^Γ] over function fields, and conjectures the same distribution over number fields via a random group model.
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The imaginary case of the nonabelian Cohen--Lenstra heuristics
The paper proves that the average number of Γ-equivariant surjections from the maximal unramified split-at-∞ Galois group onto any admissible group H is 1/[H^{Γ∞}:H^Γ] over function fields, and conjectures the same distribution over number fields via a random group model.