Low rank representations and graphs for sporadic groups [E-Book] / Cheryl E. Praeger, Leonard H. Soicher.
Praeger, Cheryl E., (author)
Soicher, Leonard H., (author)
Cambridge : Cambridge University Press, 1997
1 online resource (xi, 141 pages)
Australian Mathematical Society lecture series ; 8
Full Text
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.