Skip to content

Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6310 • Algebra

Summer 2020 • Question 9

Question

Math 6310 • Algebra Summer 2020 • Question 9

Let \(\sigma \) be the automorphism of \(\mathbb {F}_5(t)\) sending \(t\) to \(t+1\). Let \(G\) be the subgroup of \(\operatorname {Aut}(\mathbb {F}_5(t))\) generated by \(\sigma \). Find an element \(s\in \mathbb {F}_5(t)\) such that \[ \mathbb {F}_5(t)^G=\mathbb {F}_5(s). \]

Raw LaTeX

Let \(\sigma\) be the automorphism of \(\mathbb{F}_5(t)\) sending \(t\) to \(t+1\). Let \(G\) be the
subgroup of \(\operatorname{Aut}(\mathbb{F}_5(t))\) generated by \(\sigma\). Find an element
\(s\in\mathbb{F}_5(t)\) such that
\[
\mathbb{F}_5(t)^G=\mathbb{F}_5(s).
\]

Topic Tags

Finite Fields Finite Group Theory Normal Subgroups and Commutator Subgroups