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.

This is a book on combinatorial group theory.

Book Information
ISBN 9780521567374
Author Cheryl E. Praeger
Format Paperback
Page Count 156
Imprint Cambridge University Press
Publisher Cambridge University Press
Weight(grams) 240g
Dimensions(mm) 229mm * 154mm * 12mm