Low Rank Representations and Graphs for Sporadic Groups (Australian Mathematical Society Lecture Series, Series Number 8)

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. Cheryl E. Praeger, Leonard H. Soicher. Includes Bibliographical References (p. 134-138) And Index. This book addresses certain ways of representing sporadic simple groups and the graphs associated with these representations. It provides descriptions of all permutation representations of rank up to five of the sporadic groups and gives an introduction to practical computational techniques required for studying finite vertex-transitive graphs. The authors offer sufficient information about most of the groups to enable readers to reconstruct and study these representations themselves. Elementary techniques for analysis of finite vertex-transitive graphs are carefully explained, making this book not only an essential reference for experts, but also an excellent starting point for graduate students and researchers in this area. This book concerns ways of representing sporadic simple groups and about their associated graphs. It gives a classification of all low rank permutation representations of the sporadic groups, with the parameter values for all associated vertex-transitive graphs. Sufficient information is given about the groups and graphs to enable readers to re-construct and study them themselves.