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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Fall 1998 • Question 9

Question

Math 6310 • Algebra Fall 1998 • Question 9

If \(H\) is a finite group, prove that there exists a field \(k\) and a Galois extension of \(k\) with Galois group \(H\).

Raw LaTeX

If \(H\) is a finite group, prove that there exists a field \(k\) and a Galois extension of \(k\) with
Galois group \(H\).

Topic Tags

Field Extensions Finite Fields Finite Group Theory Galois Theory