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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2018 • Question 8

Question

Math 6310 • Algebra Summer 2018 • Question 8

Let \(M/K\) be a Galois extension of degree 700. Prove that there exists an intermediate field \(L\) with \([L:K]=28\). Is \(L/K\) necessarily Galois?

Raw LaTeX

Let \(M/K\) be a Galois extension of degree 700. Prove that there exists an intermediate field
\(L\) with \([L:K]=28\). Is \(L/K\) necessarily Galois?

Topic Tags

Ext Functors and Module Extensions Field Extensions Galois Theory