A NOTE ON SOME QUADRATICS AND CUBICS OVER FINITE FIELDS

Eileen X. Pan

doi:10.1017/S0004972725100671

A NOTE ON SOME QUADRATICS AND CUBICS OVER FINITE FIELDS

Eileen X. Pan

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

Abstract

We determine the conditions for the reducibility of some parametrised families of quadratic and cubic polynomials over finite fields, and count the number of irreducible trinomials. The existence of a factorisation of these polynomials plays an important role in studying the finite groups of exceptional Lie types.

Original language	English
Number of pages	8
Journal	Bulletin of the Australian Mathematical Society
DOIs	https://doi.org/10.1017/S0004972725100671
Publication status	Accepted/In press - 2025

Keywords

field theory
irreducibility of polynomials
polynomials over a finite field
trinomials

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10.1017/S0004972725100671Licence: CC BY

Cite this

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title = "A NOTE ON SOME QUADRATICS AND CUBICS OVER FINITE FIELDS",

abstract = "We determine the conditions for the reducibility of some parametrised families of quadratic and cubic polynomials over finite fields, and count the number of irreducible trinomials. The existence of a factorisation of these polynomials plays an important role in studying the finite groups of exceptional Lie types.",

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AB - We determine the conditions for the reducibility of some parametrised families of quadratic and cubic polynomials over finite fields, and count the number of irreducible trinomials. The existence of a factorisation of these polynomials plays an important role in studying the finite groups of exceptional Lie types.

KW - field theory

KW - irreducibility of polynomials

KW - polynomials over a finite field

KW - trinomials

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JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

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A NOTE ON SOME QUADRATICS AND CUBICS OVER FINITE FIELDS

Abstract

Keywords

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