Abstract
Letp be a prime and let ℚ(p) denote the maximalp-extension of ℚ. We prove that for every primep, the free pro-p group on countably many generators is realizable as a regular extension of ℚ(p)(t). As a consequence, if ℚ nil denotes the maximal nilpotent extension of ℚ, then every finite nilpotent group is realizable as a regular extension of ℚ nil (t).
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