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Finite field extension

Finite-field Frobenius automorphism

{c}
{title2=$\operatorname{Gal}(\mathbb F_{q^n}/\mathbb F_q)$}

Every <finite field extension> is a <Galois extension>, and
$$
\operatorname{Gal}(\mathbb F_{q^n}/\mathbb F_q)
=\langle x\mapsto x^q\rangle\cong C_n.
$$

Galois group of a finite field extension

Past exam of the mathematics course of the University of Cambridge / 2018 / ii / Paper 2 / 18I / Solution

Galois group of a finite field extension ( $Gal (F_{q^{n}} / F_{q})$ )

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Galois group of a finite field extension (Gal(Fqn​/Fq​))

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Galois group of a finite field extension ( $Gal (F_{q^{n}} / F_{q})$ )

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