Galois groups of polynomials arising from circulant matrices
Galois_groups_of_polynomials_arising_from_circulant_matrices.pdf (152.6Kb)Date
2008Metadata
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Computing the Galois group of the splitting field of a given polynomial with integer coeffi-
cients is a classical problem in modern algebra. A theorem of Van der Waerden [Wae] asserts
that almost all (monic) polynomials in ℤ[x] have associated Galois group S(n), the symmetric
group on n letters. Thus, cases where the associated Galois group is different from S(n) are
rare. Nevertheless, examples of polynomials where the associated Galois group is not S(n) are
well-known.
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