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  3. Low Rank Representations and Graphs for Sporadic Groups
  • Cited by 5
Publisher:
Cambridge University Press
Online publication date:
September 2009
Print publication year:
1996
Online ISBN:
9780511526039
DOI:
https://doi.org/10.1017/CBO9780511526039
Subjects:
Mathematics (general), Mathematics, Algebra
Series:
Australian Mathematical Society Lecture Series (8)
Information

Book description

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.

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