Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6320 • Algebra II

Fall 2023 • Question 4

Question

Math 6320 • Algebra II Fall 2023 • Question 4

Prove that the Galois group of an irreducible polynomial \(f(x) \in \mathbb {Q}[x]\) of degree \(p\) (a prime) with one pair of complex conjugate roots and \(p-2\) real roots is the full symmetric group \(S_p\).

Raw LaTeX

Prove that the Galois group of an irreducible polynomial
\(f(x) \in \mathbb{Q}[x]\) of degree \(p\) (a prime) with one pair of complex
conjugate roots and \(p-2\) real roots is the full symmetric group \(S_p\).

Topic Tags

Galois Groups of Polynomials Galois Theory Irreducible Polynomials Symmetric and Alternating Groups