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  3. Low Rank Representations and Graphs for Sporadic Groups
  • Cited by 5
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    • Publisher:
      Cambridge University Press
      Publication date:
      September 2009
      December 1996
      ISBN:
      9780511526039
      9780521567374
      DOI:
      https://doi.org/10.1017/CBO9780511526039
      Dimensions:
      Weight & Pages:
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.24kg, 156 Pages
      • Subjects:
      Mathematics (general), Mathematics, Algebra
      Series:
      Australian Mathematical Society Lecture Series (8)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Algebra
    Series:
    Australian Mathematical Society Lecture Series (8)
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    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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