Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-586b7cd67f-dlnhk Total loading time: 0 Render date: 2024-11-24T04:23:51.228Z Has data issue: false hasContentIssue false

5 - Uniqueness of the Steiner System S(5, 8, 24) and the Group M24

Published online by Cambridge University Press:  31 October 2024

Robert T. Curtis
Robert T. Curtis
Affiliation:
University of Birmingham
Get access

Summary

A sextet is a partition of the 24 points of Ω into six tetrads such that the union of any two of them is an octad. We find all ways in which two sextets can intersect one another and use this knowledge to force any Steiner system S(5, 8, 24) to assume the form of the one given by the MOG. In so doing we show that if a Steiner system S(5, 8, 24) exists then the order of its group of automorphisms is 244, 823, 040 and that it acts quintuply transitively on the 24 points. That the MOG does define an S(5, 8, 24) was proved in Chapter 4.

Keywords

Uniqueness of the S(5, 8, 24)sextetsthe order of M24
Type
Chapter
Information
The Art of Working with the Mathieu Group M24 , pp. 36 - 41
Publisher: Cambridge University Press
Print publication year: 2024

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×