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Realising wreath products of cyclic groups as Galois groups

Published online by Cambridge University Press:  26 February 2010

R. W. K. Odoni
R. W. K. Odoni
Affiliation:
Department of Mathematics, University of ExeterNorth Park Road, Exeter. EX4 4QE
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Extract

Let K be any field of characteristic 0 and let T and X be algebraically independent over K. For n ≥ 1 let k(n) ≥ 2 be an integer and let fn(X, T) = xk(n) + T ε K [X, T]. We shall regard T as a “parameter” and X as a “variable”. We put F1(X, T) = f1(X, T) and define, for n ≥ 1,

Type
Research Article
Information
Mathematika , Volume 35 , Issue 1 , June 1988 , pp. 101 - 113
Copyright
Copyright © University College London 1988

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References

1.Fried, M. and Jarden, M.. Field Arithmetic, Ergebnisse der Math., 3° Folge, Bd. 11 (Springer, Berlin, 1986).CrossRefGoogle Scholar
2.Grothendieck, A.. Séminaire de Géométrie Algébrique I―Révêtements étales et Groupe Fondamental, Lecture Notes in Maths., 224, (Springer, Berlin, 1971).Google Scholar
3.Hall, M.. The Theory of Groups (MacMillan, London, 1959), 81–83.Google Scholar
4.Lang, S.. Algebra (Addison-Wesley, Reading, Mass. 1965).Google Scholar
5.Lang, S.. Fundamentals of Diophantine Geometry (Springer, Berlin, 1983).CrossRefGoogle Scholar
6.Odoni, R. W. K.. The Galois theory of composites and iterates of polynomials, Proc. London Math. Soc. (3), 51 (1985), 385–414.CrossRefGoogle Scholar
7.Šafarevifč, I.. On the construction of fields with a given Galois group of order lα (in Russian). Izv. Akad Nank SSSR, Ser. Mat., 18 (1954), 26–296.Google Scholar
8.Uchida, K.. Separably Hilbertian Fields. Kodai Math. J., 3 (1980), 83–95.CrossRefGoogle Scholar
9.Zariski, O. and Samuel, P.. Commutative Algebra, vol 1 (Van Nostrand, Princeton, N.J., 1958).Google Scholar