Low Rank Representations and Graphs for Sporadic Groups

by Cheryl E. Praeger , Leonard H. Soicher

• ISBN13: 9780521567374
• ISBN10: 0521567378
• Format: Paperback
• Copyright: 1997-01-28
• Publisher: Cambridge University Press

Summary

This book presents a complete classification of the transitive permutation representations of rank at most five of the sporadic simple groups and their automorphism groups, together with a comprehensive study of the vertex-transitive graphs associated with these representations. Included is a list of all vertex-transitive, distance-regular graphs on which a sporadic almost simple group acts with rank at most five. In this list are some new, interesting distance-regular graphs of diameter two, which are not distance-transitive. For most of the representations a presentation of the sporadic group is given, with words in the given generators which generate a point stabiliser: this gives readers sufficient information to reconstruct and study the representations and graphs. Practical computational techniques appropriate for analysing finite vertex-transitive graphs are described carefully, making the book an excellent starting point for learning about groups and the graphs on which they act.

Table of Contents

1. Low rank permutation groups

2. Digraphs for transitive groups

3. The methods

4. The individual groups

5. Summary of the representations and graphs.