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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
 Format: LaTeX MathJax PDF

## 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
 MSC Classifications: 12F10 - Separable extensions, Galois theory 12F12 - Inverse Galois theory 11R32 - Galois theory 11R09 - Polynomials (irreducibility, etc.)

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