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Infinite Families of A4-Sextic Polynomials

Published online by Cambridge University Press:  20 November 2018

Joshua Ide  and
Lenny Jones
Joshua Ide
Affiliation:
Department of Mathematics, Shippensburg University, Shippensburg, PA 17257, USA e-mail: joshua.ide12@gmail.comlkjone@ship.edu
Lenny Jones
Affiliation:
Department of Mathematics, Shippensburg University, Shippensburg, PA 17257, USA e-mail: joshua.ide12@gmail.comlkjone@ship.edu
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Abstract

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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

12F1012F1211R3211R09Galois groupsextic polynomialinverse Galois theoryirreducible polynomial
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 57 , Issue 3 , 01 September 2014 , pp. 538 - 545
Copyright
Copyright © Canadian Mathematical Society 2014

References

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