AbstractWe give conditions under which the Galois group of the polynomial Xn + aX1 + b over the rational number field Q is isomorphic to the symmetric group Sn of degree n. Using the result, we prove the Williams-Uchiyama conjecture concerning the irreducibility of the polynomial Xn + X + a modulo p
It is well known that the general polynomial a_n*x^n + a_{n-1}*x^{n-₋¹} + ... + a₁x + a_0 cannot be ...
The inverse Galois problem asks whether every finite group G occurs as a Galois group over the field...
We study the problem of counting the number of roots of an irreducible polynomial $f(X) in mathbb{Z}...
AbstractWe give conditions under which the Galois group of the polynomial Xn + aX1 + b over the rati...
Computing the Galois group of the splitting field of a given polynomial with integer coefficients ov...
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 20...
AbstractIn this paper we prove that if n is an even integer or a prime number, then the Galois group...
We study abstract algebra and Hilbert's Irreducibility Theorem. We give an exposition of Galois theo...
If f(X) ∈ K[X] is a separable irreducible polynomial of degree n and Gf is its Galois group over K ...
Galois theory is an area of modern algebra which provides a framework for transforming problems invo...
Abstract: Problem Statement: Let K is the splitting field of a polynomial f(x) over a field F and αn...
The determination of polynomials over ℚ(t) with a given primitive nonsolvable permutation group of d...
It is well known that the general polynomial a_n*x^n + a_{n-1}*x^{n-₋¹} + ... + a₁x + a_0 cannot be ...
Computing the Galois group of the splitting field of a given polynomial with integer coeffi- cients ...
We define a power compositional sextic polynomial to be a monic sextic polynomial $f(x):=h(x^d)\in \...
It is well known that the general polynomial a_n*x^n + a_{n-1}*x^{n-₋¹} + ... + a₁x + a_0 cannot be ...
The inverse Galois problem asks whether every finite group G occurs as a Galois group over the field...
We study the problem of counting the number of roots of an irreducible polynomial $f(X) in mathbb{Z}...
AbstractWe give conditions under which the Galois group of the polynomial Xn + aX1 + b over the rati...
Computing the Galois group of the splitting field of a given polynomial with integer coefficients ov...
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 20...
AbstractIn this paper we prove that if n is an even integer or a prime number, then the Galois group...
We study abstract algebra and Hilbert's Irreducibility Theorem. We give an exposition of Galois theo...
If f(X) ∈ K[X] is a separable irreducible polynomial of degree n and Gf is its Galois group over K ...
Galois theory is an area of modern algebra which provides a framework for transforming problems invo...
Abstract: Problem Statement: Let K is the splitting field of a polynomial f(x) over a field F and αn...
The determination of polynomials over ℚ(t) with a given primitive nonsolvable permutation group of d...
It is well known that the general polynomial a_n*x^n + a_{n-1}*x^{n-₋¹} + ... + a₁x + a_0 cannot be ...
Computing the Galois group of the splitting field of a given polynomial with integer coeffi- cients ...
We define a power compositional sextic polynomial to be a monic sextic polynomial $f(x):=h(x^d)\in \...
It is well known that the general polynomial a_n*x^n + a_{n-1}*x^{n-₋¹} + ... + a₁x + a_0 cannot be ...
The inverse Galois problem asks whether every finite group G occurs as a Galois group over the field...
We study the problem of counting the number of roots of an irreducible polynomial $f(X) in mathbb{Z}...
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