Low Rank Representations and Graphs for Sporadic Groups
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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 grou...
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.
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.
This is a book on combinatorial group theory.
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.
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.
This is a book on combinatorial group theory.
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