We prove that a free profinite (pro-p) product over a set converging to 1 of countably many Demushkin groups of rank ₀, Gᵢ, that can be realized as absolute Galois groups, is isomorphic to an absolute Galois group if and only if logₚq(Gᵢ)→ ∞.
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Tamar Bar‐On (2024) studied this question.
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