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A group-theoretical property of the ramification filtration. (English. Russian original) Zbl 0929.11056
Izv. Math. 62, No. 6, 1073-1094 (1998); translation from Izv. Ross. Akad. Nauk, Ser.Mat. 62, No. 6, 3-26 (1998).
Let $$\Gamma(p)$$ be the Galois group of the maximal $$p$$-extension of a complete discrete valuation field with a perfect residue field of characteristic $$p>0$$. Let $$v>-1$$ and let $$\Gamma (p)^{(v)}$$ be the ramification subgroup of $$\Gamma(p)$$ in the upper numbering. The author proves that any closed non-open finitely generated subgroup of the quotient $$\Gamma(p)/ \Gamma(p)^{(v)}$$ is a free pro-$$p$$-group.
Reviewer: H.Koch (Berlin)
MSC:
 11S15 Ramification and extension theory
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