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Search: MSC category 12F10 ( Separable extensions, Galois theory )

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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 2014 (vol 57 pp. 735)

Cagliero, Leandro; Szechtman, Fernando
 On the Theorem of the Primitive Element with Applications to the Representation Theory of Associative and Lie Algebras We describe of all finite dimensional uniserial representations of a commutative associative (resp. abelian Lie) algebra over a perfect (resp. sufficiently large perfect) field. In the Lie case the size of the field depends on the answer to following question, considered and solved in this paper. Let $K/F$ be a finite separable field extension and let $x,y\in K$. When is $F[x,y]=F[\alpha x+\beta y]$ for some non-zero elements $\alpha,\beta\in F$? Keywords:uniserial module, Lie algebra, associative algebra, primitive elementCategories:17B10, 13C05, 12F10, 12E20

3. CMB 2002 (vol 45 pp. 422)

Ledet, Arne
 On the Essential Dimension of Some Semi-Direct Products We give an upper bound on the essential dimension of the group $\mathbb{Z}/q\rtimes(\mathbb{Z}/q)^*$ over the rational numbers, when $q$ is a prime power. Category:12F10

4. 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