Infinite Families of $A_4$-Sextic Polynomials

Canadian mathematical bulletin

Joshua Ide¹  Lenny Jones¹ 

[1] Department of Mathematics, Shippensburg University, Shippensburg, PA 17257, USA

关键词: Galois group;    sextic polynomial;    inverse Galois theory;    irreducible polynomial;   

DOI  :  10.4153/CMB-2014-008-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

In this article we develop a test to determine whether a sexticpolynomial that is irreducible over $mathbb{Q}$ has Galois group isomorphicto the alternating group $A_4$. This test does not involve thecomputation of resolvents, and we use this test to construct severalinfinite families of such polynomials.

【 授权许可】

Unknown