Geodesic
On the algebraic closure of a local field for $p=2$
Izvestiya. Mathematics, Tome 6 (1972) no. 5, pp. 925-937 
I. G. Zel'venskii. On the algebraic closure of a local field for $p=2$. Izvestiya. Mathematics, Tome 6 (1972) no. 5, pp. 925-937. http://geodesic.mathdoc.fr/item/IM2_1972_6_5_a1/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Let $k$ be a finite extension of the field of 2-adic numbers. In this paper we determine the structure of the Galois groups of the algebraic closure and of the maximal extension without simple ramification of the field $k$ under the assumption that the maximal extension without higher ramification of the field $k$ contains a fourth root of 1.

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