Journal ArticleDOI
Polynomials with galois group psl(2,7)
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This article is published in Communications in Algebra.The article was published on 1980-01-01. It has received 32 citations till now. The article focuses on the topics: Galois group & Embedding problem.read more
Citations
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Book ChapterDOI
Deforming Galois Representations
TL;DR: In this paper, the Galois group of the maximal algebraic extension of ℚ unramified outside the finite set S of primes of the continuous homomorphism ρ to p-adic representations is studied.
Journal Article
Galois theory, elliptic curves, and root numbers
TL;DR: In this article, the root number problem is considered in the context of Galois theory, where the inverse problem is to find arithmetical realizations of the irreducible representations of the root numbers.
Journal ArticleDOI
Computing Galois groups over the rationals
Leonard H. Soicher,John McKay +1 more
TL;DR: In this paper, practical computational techniques are described to determine the Galois group of a polynomial over the rationals, and each transitive permutation group of degree 3 to 7 is realized as a Galois groups over rationals.
Journal ArticleDOI
Galois representations with open image
TL;DR: In this paper, an approach to constructing Galois extensions of Q with Galois group isomorphic to an open subgroup of GL_n({\mathbf{Z}}_p) for various values of n and primes p.
References
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BookDOI
Lehrbuch der algebra
TL;DR: In this article, the Galois's Theoretic Theorem 3.2.1.1 is used to describe the transformation of the Wurzeln algebraic Gleichungs.
Journal ArticleDOI
On the construction of Galois extensions of function fields and number fields
TL;DR: In this paper, it was shown that if p is an odd prime such that 2, 3 or 7 is a quadratic non-residue modulo p, then PSL2(Z/pZ ) occurs as Galois groups over the rationals.
Journal ArticleDOI
Ueber die Auflösung gewisser Gleichungen vom siebenten und achten Grade
Journal ArticleDOI
Polynomials with PSL(2, 7) as Galois group
TL;DR: In this article, a technique for determining the set-transitivity of the Galois group of a polynomial over the rationals was described, and a short proof was given that the Polynomial P7(x) = x7 − 154x + 99 has the simple group PSL(2, 7) of order 168 as its group over rationals.