Polynomial time algorithms for Galois groups

  • Susan Landau
Computational Group Theory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 174)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1984

Authors and Affiliations

  • Susan Landau
    • 1
  1. 1.Math DepartmentWesleyan UniversityMiddletown

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