# On Elkies' method for bounding the transitivity degree of Galois groups

## TL;DR

This paper explores Elkies' method for bounding Galois group transitivity, applying it to verify the monodromy group of a specific cover matches the sporadic Conway group Co3, demonstrating its practical utility.

## Contribution

It extends Elkies' technique to new applications, notably confirming the isomorphism of a monodromy group with a sporadic simple group.

## Key findings

- Successfully verified the monodromy group as Co3
- Demonstrated the effectiveness of Elkies' method in complex cases
- Provided new applications for bounding Galois group transitivity

## Abstract

In 2013 Elkies described a method for bounding the transitivity degree of Galois groups. Our goal is to give additional applications of this technique, in particular verifying that the monodromy group of the degree-276 cover defined over a degree-12 number field computed by Monien is isomorphic to the sporadic Conway group Co3.