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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 2019 • Question 2

Question

Math 6310 • Algebra Fall 2019 • Question 2

Determine the splitting field of the polynomial \(x^p-x-a\) over \(\mathbb {F}_p\) where \(0\ne a\in \mathbb {F}_p\). Show that the Galois group is cyclic.

Raw LaTeX

Determine the splitting field of the polynomial \(x^p-x-a\) over \(\mathbb{F}_p\) where
\(0\ne a\in\mathbb{F}_p\). Show that the Galois group is cyclic.

Topic Tags

Finite Fields Galois Groups of Polynomials Galois Theory Splitting Fields