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Izv. RAN. Ser. Mat., 1998, Volume 62, Issue 6, Pages 3–26 (Mi izv218)  

This article is cited in 1 scientific paper (total in 1 paper)

A group-theoretical property of the ramification filtration

V. A. Abrashkin

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: 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 $p>0$. If $v_0>-1$ and $\Gamma(p)^{(v_0)}$ is the ramification subgroup of $\Gamma(p)$ in the upper numbering, we prove that any closed non-open finitely generated subgroup of the quotient $\Gamma(p)/\Gamma(p)^{(v_0)}$ is a free pro-$p$-group. In particular, this quotient has no torsion and no non-trivial commuting elements.

DOI: https://doi.org/10.4213/im218

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English version:
Izvestiya: Mathematics, 1998, 62:6, 1073–1094

Bibliographic databases:

MSC: 11S15
Received: 05.01.1997

Citation: V. A. Abrashkin, “A group-theoretical property of the ramification filtration”, Izv. RAN. Ser. Mat., 62:6 (1998), 3–26; Izv. Math., 62:6 (1998), 1073–1094

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. Snopce I., Zalesskii P.A., “Subgroup Properties of Demushkin Groups”, Math. Proc. Camb. Philos. Soc., 160:1 (2016), 1–9  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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