Geodesic
A~group-theoretical property of the ramification filtration
Izvestiya. Mathematics , Tome 62 (1998) no. 6, pp. 1073-1094

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1998_62_6_a0,
     author = {V. A. Abrashkin},
     title = {A~group-theoretical property of the ramification filtration},
     journal = {Izvestiya. Mathematics },
     pages = {1073--1094},
     publisher = {mathdoc},
     volume = {62},
     number = {6},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a0/}
}
TY  - JOUR
AU  - V. A. Abrashkin
TI  - A~group-theoretical property of the ramification filtration
JO  - Izvestiya. Mathematics 
PY  - 1998
SP  - 1073
EP  - 1094
VL  - 62
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a0/
LA  - en
ID  - IM2_1998_62_6_a0
ER  - 
%0 Journal Article
%A V. A. Abrashkin
%T A~group-theoretical property of the ramification filtration
%J Izvestiya. Mathematics 
%D 1998
%P 1073-1094
%V 62
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a0/
%G en
%F IM2_1998_62_6_a0
V. A. Abrashkin. A~group-theoretical property of the ramification filtration. Izvestiya. Mathematics , Tome 62 (1998) no. 6, pp. 1073-1094. http://geodesic.mathdoc.fr/item/IM2_1998_62_6_a0/