Belyi map for the sporadic group J2

TL;DR

This paper constructs a genus 0 Belyi map associated with the sporadic Janko group J2, leading to a polynomial with a specific Galois group over a number field, advancing the understanding of algebraic curves and Galois theory.

Contribution

It introduces a genus 0 Belyi map for J2, providing new explicit examples linking sporadic groups to Galois representations.

Findings

Constructed a genus 0 Belyi map for J2

Derived a polynomial with Aut(J2) as Galois group over a degree 10 number field

Establishes connections between sporadic groups and Galois theory

Abstract

We present a genus 0 Belyi map for the sporadic Janko group J2 of degree 280. As a consequence we obtain a polynomial having Aut(J2) as a Galois group over K(t) where K is a number field of degree 10.