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Construction of semiabelian Galois extensions

Published online by Cambridge University Press:  18 May 2009

Michael Stoll
Affiliation:
Mathematisches Institut Der UniversitätBeringstr. 4, D-53115 Bonn, 〈stoll@rhein.iam.uni-bonn.de〉
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This paper shows how to construct Galois field extensions of Hilbertian fields with a given group out of some subclass (called ‘semiabelian groups’ by Matzat [2]) of all soluble groups as Galois group. This is done in a fairly explicit way by constructing polynomials whose Galois groups are universal in the sense that every group in the above subclass is obtained as a quotient of some of them.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1995

References

1.Dentzer, Ralf, On split embedding problems with abelian kernel, Preprint 91–10, Interdisziplinäres Zentrum für wissenschaftliches Rechnen, Universität Heidelberg (1991).Google Scholar
2.Matzat, B. Heinrich, Der Kenntnisstand in der konstruktiven Galoisschen Theorie, Preprint 90–18, Interdisziplinäres Zentrum für wissenschaftliches Rechnen, Universität Heidelberg (1990), or: PM 95 (1991), 6598, Birkhäuser-Verlag.Google Scholar
3.Odoni, R. W. K., The Galois theory of iterates and composites of polynomials, Proc. London Math. Soc. (3), 51 (1985), 385414.CrossRefGoogle Scholar
4.Odoni, R. W. K., Realising wreath products of cyclic groups as Galois groups, Mathematika 35 (1988), 101113.CrossRefGoogle Scholar
5.Stoll, Michael, Galois groups over of some iterated polynomials, Arch. Math. 59 (1992), 239244.CrossRefGoogle Scholar
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