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Search: All articles in the CMB digital archive with keyword Galois group

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1. CMB 2014 (vol 57 pp. 538)

Ide, Joshua; Jones, Lenny
 Infinite Families of $A_4$-Sextic Polynomials 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 polynomialCategories:12F10, 12F12, 11R32, 11R09

2. CMB 2001 (vol 44 pp. 313)

 Images of mod $p$ Galois Representations Associated to Elliptic Curves We give an explicit recipe for the determination of the images associated to the Galois action on $p$-torsion points of elliptic curves. We present a table listing the image for all the elliptic curves defined over $\QQ$ without complex multiplication with conductor less than 200 and for each prime number~$p$. Keywords:Galois groups, elliptic curves, Galois representation, isogenyCategories:11R32, 11G05, 12F10, 14K02