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Computational methods in constructive Galois theory

  • B. Heinrich Matzat
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 296)

Abstract

This lecture can be viewed as a complement to my lecture [18] given in Berkeley. It begins with a short survey of the known rationality criteria for Galois extensions over ℂ(t1,...,ts) or, equivalently, for Galois coverings of the projective space ℙS(ℂ). In the subsequent sections some computational problems are discussed, which arise in the application of these theorems: computation of class numbers of generators of finite groups, computation of the braid orbits on classes of generators, construction of polynomials with given ramification structure, determination of Galois groups. The computational methods are examplified by the Mathieu groups M11,...,M24. So polynomials with Galois group M11,M12,M22 over ℚ are constructed and the existence of Galois extensions with Galois group M24 over ℚ is proved.

Keywords

Finite Group Maximal Subgroup Galois Group Class Number Braid Group 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • B. Heinrich Matzat
    • 1
  1. 1.Fachbereich Mathematik, TU BerlinBerlin 12

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