On the n-torsion subgroup of the Brauer group of a number field
Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 199-204.

Pour toute extension galoisienne K de et tout entier positif n premier au nombre de classes de K, il existe une extension abélienne L de K d’exposant n telle que le n-sous-groupe de torsion du groupe de Brauer de K est égal au groupe de Brauer relatif de L/K.

Given a number field K Galois over the rational field , and a positive integer n prime to the class number of K, there exists an abelian extension L/K (of exponent n) such that the n-torsion subgroup of the Brauer group of K is equal to the relative Brauer group of L/K.

@article{JTNB_2003__15_1_199_0,
     author = {Kisilevsky, Hershy and Sonn, Jack},
     title = {On the $n$-torsion subgroup of the {Brauer} group of a number field},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {199--204},
     publisher = {Universit\'e Bordeaux I},
     volume = {15},
     number = {1},
     year = {2003},
     zbl = {1048.11089},
     mrnumber = {2019011},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2003__15_1_199_0/}
}
TY  - JOUR
AU  - Kisilevsky, Hershy
AU  - Sonn, Jack
TI  - On the $n$-torsion subgroup of the Brauer group of a number field
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2003
DA  - 2003///
SP  - 199
EP  - 204
VL  - 15
IS  - 1
PB  - Université Bordeaux I
UR  - http://www.numdam.org/item/JTNB_2003__15_1_199_0/
UR  - https://zbmath.org/?q=an%3A1048.11089
UR  - https://www.ams.org/mathscinet-getitem?mr=2019011
LA  - en
ID  - JTNB_2003__15_1_199_0
ER  - 
Kisilevsky, Hershy; Sonn, Jack. On the $n$-torsion subgroup of the Brauer group of a number field. Journal de Théorie des Nombres de Bordeaux, Tome 15 (2003) no. 1, pp. 199-204. http://www.numdam.org/item/JTNB_2003__15_1_199_0/

[1] E. Aljadeff, J. Sonn, Relative Brauer groups and m-torsion. Proc. Amer. Math. Soc. 130 (2002), 1333-1337. | MR 1879954 | Zbl 01721035

[2] B. Fein, M. Schacher, Relative Brauer groups I. J. Reine Angew. Math. 321 (1981), 179-194. | MR 597988 | Zbl 0436.13003

[3] B. Fein, W. Kantor, M. Schacher, Relative Brauer groups II. J. Reine Angew. Math. 328 (1981), 39-57. | MR 636194 | Zbl 0457.13004

[4] B. Fein, M. Schacher, Relative Brauer groups III. J. Reine Angew. Math. 335 (1982), 37-39. | MR 667461 | Zbl 0484.13005