MÖBIUS–FROBENIUS MAPS ON IRREDUCIBLE POLYNOMIALS

DOI10.1017/S0004972720001306zbMATH Open1472.11298arXiv1812.08900OpenAlexW3112781117MaRDI QIDQ4999616

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Publication date: 7 July 2021

Published in: Bulletin of the Australian Mathematical Society (Search for Journal in Brave)

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 $extPGammaextL(2,q^n)=extPGL(2,q^n)timesextGal(mathbb{F}_{q^n}/mathbb{F}_q)$ 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.

Full work available at URL: https://arxiv.org/abs/1812.08900

zbMATH Keywords

fixed pointgroup actionenumeration formulairreducible polynomials over finite fields

Mathematics Subject Classification ID

Polynomials over finite fields (11T06) Finite fields (field-theoretic aspects) (12E20)

Cites Work

• On the action of \(\text{GL}_2(\mathbb F_q)\) on irreducible polynomials over \(\mathbb F_q\)
• Factorization of a class of polynomials over finite fields
• Self-conjugate-reciprocal irreducible monic factors of \(x^{n}-1\) over finite fields and their applications
• The action of \(\mathrm{GL}_2(\mathbb{F}_q)\) on irreducible polynomials over \(\mathbb{F}_q\), revisited
• Generalizations of self-reciprocal polynomials
• Self-reciprocal polynomials over finite fields

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