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articleNo Access
A Class of Trinomials with Galois Group S_n
- Anuj Bishnoi and
- Sudesh K. Khanduja
Algebra Colloquium31 Oct 2012
Preview Abstract
A well known result of Schur states that if n is a positive integer and a₀, a₁,…,a_n are arbitrary integers with a₀a_n coprime to n!, then the polynomial is irreducible over the field ℚ of rational numbers. In case each a_i = 1, it is known that the Galois group of f_n(x) over ℚ contains A_n, the alternating group on n letters. In this paper, we extend this result to a larger class of polynomials f_n(x) which leads to the construction of trinomials of degree n for each n with Galois group S_n, the symmetric group on n letters.

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