Low Rank Representations and Graphs for Sporadic Groups

Erscheinungsjahr 2003
ISBN: 978-0-521-56737-4
Verlag: Cambridge University Press

Buch, Englisch, Band 8, 153 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 237 g

Reihe: Australian Mathematical Society Lecture Series

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.

Autoren/Hrsg.

Praeger, Cheryl E.

Soicher, Leonard H.

Loxton, J. H.

Heyde, C. C.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

1. Low rank permutation groups; 2. Digraphs for transitive groups; 3. The methods; 4. The individual groups; 5. Summary of the representations and graphs.