×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI