Computing the Fixed Field of $\text{Aut}(\mathbb{F}(x)/\mathbb{F})$

zbMATH Open1384.12001arXiv1612.01226MaRDI QIDQ4636326

Author name not available (Why is that?)

Publication date: 23 April 2018

Abstract: For a finite field

m a t h b b F

, it is a basic result of Galois theory that the fixed field

E

of

e x t A u t (m a t h b b F (x) / m a t h b b F)

is a proper extension of

m a t h b b F

. In this expository paper we construct, for all finite fields, an element

f i n m a t h b b F (x)

such that

E = m a t h b b F (f)

. This element is shown to be easily computable in all cases using a simple formula. The approach is entirely elementary, and aimed at the student level; only a basic familiarity with Galois theory and field extensions is assumed.

Full work available at URL: https://arxiv.org/abs/1612.01226

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