Look Inside The Maximal Subgroups of the Low-Dimensional Finite Classical Groups

The Maximal Subgroups of the Low-Dimensional Finite Classical Groups

Part of London Mathematical Society Lecture Note Series

Authors:
John N. Bray, Queen Mary University of London
Derek F. Holt, University of Warwick
Colva M. Roney-Dougal, University of St Andrews, Scotland

Date Published: July 2013
availability: Available
format: Paperback
isbn: 9780521138604

Rate & review

Paperback

Add to wishlist

Other available formats:
eBook

Looking for an inspection copy?

This title is not currently available on inspection

Description

This book classifies the maximal subgroups of the almost simple finite classical groups in dimension up to 12; it also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q). Theoretical and computational tools are used throughout, with downloadable Magma code provided. The exposition contains a wealth of information on the structure and action of the geometric subgroups of classical groups, but the reader will also encounter methods for analysing the structure and maximality of almost simple subgroups of almost simple groups. Additionally, this book contains detailed information on using Magma to calculate with representations over number fields and finite fields. Featured within are previously unseen results and over 80 tables describing the maximal subgroups, making this volume an essential reference for researchers. It also functions as a graduate-level textbook on finite simple groups, computational group theory and representation theory.
- Results are listed in clear and concise tables, easy to use and cite
- Some results presented within are not previously known
- Brings together information on analysing representations of quasisimple groups into one comprehensive source
Read more
Reviews & endorsements
'The study of the maximal subgroups of the finite classical groups started long ago. Their understanding has been crucial in the work on the classification of finite simple groups. The methods [in this book] efficiently combine theoretical techniques together with computer algebra systems (GAP, Magma), with the computational files available [online] … The theoretical literature on the subject is highly exploited, especially Aschbacher's results which describe the maximal subgroups of most of the finite almost simple classical groups … The tables are packed with a great amount of information, and should satisfy the reader who is looking for some specific information about the structure of the maximal subgroups of a given classical group.' Nadia P. Mazza, Mathematical Reviews

Customer reviews

Not yet reviewed
Be the first to review

Log in to review

Review was not posted due to profanity
×

, create a review

(If you're not , sign out)

Please enter the right captcha value

Please enter a star rating.

Your review must be a minimum of 12 words.

How do you rate this item?

Reviews must contain at least 12 words about the product.

×

Product details
- Date Published: July 2013
- format: Paperback
- isbn: 9780521138604
- length: 452 pages
- dimensions: 228 x 152 x 23 mm
- weight: 0.64kg
- contains: 100 tables 20 exercises
- availability: Available
Table of Contents
Preface
1. Introduction
2. The main theorem, and types of geometric subgroups
3. Geometric maximal subgroups
4. Groups in class S: cross characteristic
5. Groups in Class S: defining characteristic
6. Containments involving S-subgroups
7. Maximal subgroups of exceptional groups
8. Tables.
Look Inside
Resources for

The Maximal Subgroups of the Low-Dimensional Finite Classical Groups

John N. Bray, Derek F. Holt, Colva M. Roney-Dougal
General Resources
- Computer code files
- Errata
Find resources associated with this title
Back to resources home

Your search for '' returned .
Type Name Unlocked * Format Size

Showing of

Back to top

This title is supported by one or more locked resources. Access to locked resources is granted exclusively by Cambridge University Press to lecturers whose faculty status has been verified. To gain access to locked resources, lecturers should sign in to or register for a Cambridge user account.

Please use locked resources responsibly and exercise your professional discretion when choosing how you share these materials with your students. Other lecturers may wish to use locked resources for assessment purposes and their usefulness is undermined when the source files (for example, solution manuals or test banks) are shared online or via social networks.

Supplementary resources are subject to copyright. Lecturers are permitted to view, print or download these resources for use in their teaching, but may not change them or use them for commercial gain.

If you are having problems accessing these resources please contact lecturers@cambridge.org.
Authors
John N. Bray, Queen Mary University of London
John Bray obtained a PhD from the University of Birmingham in 1997, which was followed by postdoctoral positions at Birmingham and Queen Mary. He has held a lectureship at Queen Mary, University of London, since 2007. He is heavily involved with the online web-atlas of group representations, a popular resource in the group theory community.
Derek F. Holt, University of Warwick
Derek Holt has been at the University of Warwick since 1978, where he was made a professor in 2001. He has been active in group theory research for over 40 years and has over 100 publications to his name. He was awarded the LMS Junior Whitehead Prize in 1981 for his solution to the long-standing problem of classifying groups with more than one end. He has co-authored several books including the influential graduate text Handbook of Computational Group Theory (2005). He is Editor-in-Chief of the London Mathematical Society Journal of Computation and Mathematics, and is on the editorial board of several other journals.
Colva M. Roney-Dougal, University of St Andrews, Scotland
Colva Roney-Dougal received a PhD from Queen Mary, University of London, in 2001, following which she held postdoctoral positions in Sydney and St Andrews. She has been a lecturer at St Andrews since 2005 and was appointed to Senior Lecturer in 2010. Her research on the classification of primitive permutation groups has been turned into highly-used databases in MAGMA and GAP. In addition, she is heavily involved in the popularisation of mathematics, and in this capacity is a regular presence on Radio 4's 'In Our Time' with Melvyn Bragg, as well as other national radio shows.