Geodesic
Cohomological dimension of some Galois groups
Izvestiya. Mathematics, Tome 9 (1975) no. 3, pp. 455-463 Cet article a éte moissonné depuis la source Math-Net.Ru

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Suppose that $l$ is a prime number, $k$ is an algebraic number field containing a primitive root $\zeta_l$ ($\zeta_4$ if $l=2$), $S$ is a finite set of places of $k$ which contains all divisors of $l$, $K$ is the maximal $l$-extension of $k$ unramified outside $S$, $k_\infty$ is an arbitrary $\Gamma$-extension of $k$, and $H=G(K/k_\infty$. In this paper we find necessary and sufficient conditions for the group $H$ to be a free pro-$l$-group. We also obtain a description of all $\Gamma$-extensions $k_\infty/k$ having the property that any place of $k$ has a finite number of extensions to $k_\infty$. We prove that, in some sense, such $\Gamma$-extensions make up the overwhelming majority of all $\Gamma$-extensions. Bibliography: 4 items. 
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     author = {L. V. Kuz'min},
     title = {Cohomological dimension of some {Galois} groups},
     journal = {Izvestiya. Mathematics},
     pages = {455--463},
     year = {1975},
     volume = {9},
     number = {3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1975_9_3_a1/}
}
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%A L. V. Kuz'min
%T Cohomological dimension of some Galois groups
%J Izvestiya. Mathematics
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L. V. Kuz'min. Cohomological dimension of some Galois groups. Izvestiya. Mathematics, Tome 9 (1975) no. 3, pp. 455-463. http://geodesic.mathdoc.fr/item/IM2_1975_9_3_a1/

[1] Kuzmin L. V., “Modul Teita polei algebraicheskikh chisel”, Izv. AN SSSR. Ser. matem., 36 (1972), 267–327 | MR

[2] Iwasawa K., “On the $\mu$-invariants of $\mathbf{Z}l$-extensions”, Number theory, algebraic geometry and commutative algebra in honour Akizuki, Tokyo, 1973, 1–1 | MR | Zbl

[3] Kox X., Teoriya Galua $p$-rasshirenii, Mir, M., 1973 | MR

[4] Brumer A., “Galois groups of extensions of algebraic number fields with given ramification”, Mich. Math. J., 13:1 (1966), 33–40 | DOI | MR | Zbl