Abstract
In this paper we present several polynomial time algorithms for Galois groups. We show:
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(i)
There are polynomial time algorithms to determine:
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(a)
If the Galois group of an irreducible polynomial over Q is a p-group.
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(b)
the prime divisors of the order of a solvable Galois group
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(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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© 1984 Springer-Verlag Berlin Heidelberg
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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
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