8 problems. Fall 2007, problems 5–6 Conditions for f(x^p) to be a p-th power in characteristic p Quadratic extensions and Galois behavior in characteristic 2 Fall 2009, problems 3–5 Minimal polynomial degree for an algebraic element over a finite field Every finite group appears as a Galois group over some field extension Splitting field and Galois group of \(x^4-5\) over \(\QQ\) Spring 2008, problem 4 Structure of Galois group when an intermediate field has degree 2 Spring 2009, problems 4–5 Galois group of the splitting field of sqrt(2 + sqrt(2)) over Q F-isomorphic intermediate fields correspond to conjugate subgroups of the Galois group Browse these problems in source order