Abstract
In this final section, we show how to compute Galois groups of polynomials of low degree over ℚ. Recall that the Galois group of a polynomial of degree n is a subgroup of S n (regarded as the group of all permutations of the roots). Of course, just as there are some permutations of the vertices of a polygon that do not arise from symmetries, so, too, some permutations of the roots of a polynomial may have nothing to do with field automorphisms.
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© 1998 Springer Science+Business Media New York
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Rotman, J. (1998). Galois Groups of Quadratics, Cubics, and Quartics. In: Galois Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0617-0_20
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DOI: https://doi.org/10.1007/978-1-4612-0617-0_20
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-98541-1
Online ISBN: 978-1-4612-0617-0
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