JP Journal of Algebra, Number Theory and Applications
Volume 39, Issue 5, Pages 685 - 702
(October 2017) http://dx.doi.org/10.17654/NT039050685 |
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DETERMINING GALOIS GROUPS OF REDUCIBLE POLYNOMIALS VIA DISCRIMINANTS AND LINEAR RESOLVENTS
Chad Awtrey, Taylor Cesarski and Peter Jakes
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Abstract: Let be a polynomial with integer coefficients of degree less than or equal to 7, and assume f to be reducible over the rational numbers. We show how to compute the Galois group of f. The main tools we employ are composita of irreducible factors, discriminants, and in the case when f is a degree 7 polynomial, two linear resolvents. For each possible Galois group G, we provide a reducible polynomial whose Galois group over the rationals is G. |
Keywords and phrases: reducible polynomials, Galois groups, discriminants, linear resolvents. |
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