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arXiv · 1812.08900

M\"obius-Frobenius maps on irreducible polynomials

F. E. Brochero Martínez·Daniela Oliveira·Lucas Reis
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Abstract

Let $n$ be a positive integer and let $\mathbb F_{q^n}$ be the finite field with $q^n$ elements, where $q$ is a power of a prime. This paper introduces a natural action of the Projective Semilinear Group $\text{P}\Gamma \text{L}(2, q^n)=\text{PGL}(2, q^n)\rtimes \text{Gal}(\mathbb{F}_{q^n}/\mathbb{F}_q)$ on the set of monic irreducible polynomials over the finite field $\mathbb{F}_{q^n}$. Our main results provide information on the characterization and number of fixed points.

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BibTeXRIS

F. E. Brochero Martínez, Daniela Oliveira, Lucas Reis. 2018-12-21. M\"obius-Frobenius maps on irreducible polynomials. https://arxiv.org/abs/1812.08900

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