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Infinite Families of $A_4$-Sextic Polynomials

  Published:2014-04-15
 Printed: Sep 2014
  • Joshua Ide,
    Department of Mathematics, Shippensburg University, Shippensburg, PA 17257, USA
  • Lenny Jones,
    Department of Mathematics, Shippensburg University, Shippensburg, PA 17257, USA
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Abstract

In this article we develop a test to determine whether a sextic polynomial that is irreducible over $\mathbb{Q}$ has Galois group isomorphic to the alternating group $A_4$. This test does not involve the computation of resolvents, and we use this test to construct several infinite families of such polynomials.
Keywords: Galois group, sextic polynomial, inverse Galois theory, irreducible polynomial Galois group, sextic polynomial, inverse Galois theory, irreducible polynomial
MSC Classifications: 12F10, 12F12, 11R32, 11R09 show english descriptions Separable extensions, Galois theory
Inverse Galois theory
Galois theory
Polynomials (irreducibility, etc.)
12F10 - Separable extensions, Galois theory
12F12 - Inverse Galois theory
11R32 - Galois theory
11R09 - Polynomials (irreducibility, etc.)
 

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