DETERMINING GALOIS GROUPS OF REDUCIBLE POLYNOMIALS VIA DISCRIMINANTS AND LINEAR RESOLVENTS

@article{Awtrey2017DETERMININGGG,
  title={DETERMINING GALOIS GROUPS OF REDUCIBLE POLYNOMIALS VIA DISCRIMINANTS AND LINEAR RESOLVENTS},
  author={C. Awtrey and Taylor Cesarski and P. Jakes},
  journal={JP journal of algebra, number theory and applications},
  year={2017},
  volume={39},
  pages={685-702}
}
Let f(x) be a polynomial with integer coe cients of degree less than or equal to 7, and assume f is 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. 

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