Generalized cyclotomic fields
Beale, Stephen ; Harrison, D. K.
Illinois J. Math., Tome 33 (1989) no. 4, p. 691-703 / Harvested from Project Euclid
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This note examines the splitting field $K \subseteq \mathbf{C}$ over $\mathbf{Q}$ of the set of polynomials of the form $X^{n}-b$, with $n \in \mathbf{N}^{\ast}$ and $b \in \mathbf{Q}$.We obtain the Galois group $\mathrm{Aut}_{\mathbf{Q}}(K)$ as a natural subgroup of a semidirect product of the Pontryagin dual of a quotient of the divisible hull of the positive rationals and the automorphism group of the maximal abelian extension of the rationals.
Publié le : 1989-12-15
Classification:  12F10,  11R32 
@article{1255988579,
     author = {Beale, Stephen and Harrison, D. K.},
     title = {Generalized cyclotomic fields},
     journal = {Illinois J. Math.},
     volume = {33},
     number = {4},
     year = {1989},
     pages = { 691-703},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1255988579}
}

Beale, Stephen; Harrison, D. K. Generalized cyclotomic fields. Illinois J. Math., Tome 33 (1989) no. 4, pp.  691-703. http://gdmltest.u-ga.fr/item/1255988579/