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International Symposium on Symbolic and Algebraic Manipulation

EUROSAM 1984: EUROSAM 84 pp 225–236Cite as

Polynomial time algorithms for Galois groups

  • Computational Group Theory
  • Conference paper
  • First Online:

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 174))

Abstract

In this paper we present several polynomial time algorithms for Galois groups. We show:

  1. (i)

    There are polynomial time algorithms to determine:

  1. (a)

    If the Galois group of an irreducible polynomial over Q is a p-group.

  2. (b)

    the prime divisors of the order of a solvable Galois group

  3. (ii)

    Using the classification theorem for finite simple groups, there is a polynomial time algorithm to determine whether an irreducible polynomial over Q has Galois group Sn or An.

We consider several techniques for computing Galois groups, including the Chebatorev Density Theorem, and their applicability to polynomial time computations.

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References

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Author information

Authors and Affiliations

  1. Math Department, Wesleyan University, 06457, Middletown, CT.

    Susan Landau

Authors
  1. Susan Landau
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Editor information

John Fitch

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© 1984 Springer-Verlag Berlin Heidelberg

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Cite this paper

Landau, S. (1984). Polynomial time algorithms for Galois groups. In: Fitch, J. (eds) EUROSAM 84. EUROSAM 1984. Lecture Notes in Computer Science, vol 174. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0032845

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  • DOI: https://doi.org/10.1007/BFb0032845

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-13350-6

  • Online ISBN: 978-3-540-38893-7

  • eBook Packages: Springer Book Archive

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