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  3. Geometry of Sporadic Groups
  • Cited by 12
      • Volume 1: Petersen and Tilde Geometries
      • A. A. Ivanov, Imperial College of Science, Technology and Medicine, London
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    • Publisher:
      Cambridge University Press
      Publication date:
      January 2010
      June 1999
      ISBN:
      9780511525933
      9780521413626
      9780521062831
      DOI:
      https://doi.org/10.1017/CBO9780511525933
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.705kg, 424 Pages
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.642kg, 424 Pages
      • Subjects:
      Mathematics (general), Mathematics, Real and Complex Analysis, Algebra
      Series:
      Encyclopedia of Mathematics and its Applications (76)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Real and Complex Analysis, Algebra
    Series:
    Encyclopedia of Mathematics and its Applications (76)
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    Book description

    This book is the first volume in a two-volume set, which will provide the complete proof of classification of two important classes of geometries, closely related to each other: Petersen and tilde geometries. There is an infinite family of tilde geometries associated with non-split extensions of symplectic groups over a field of two elements. Besides that there are twelve exceptional Petersen and tilde geometries. These exceptional geometries are related to sporadic simple groups, including the famous Monster group and this volume gives a construction for each of the Petersen and tilde geometries which provides an independent existence proof for the corresponding automorphism group. Important applications of Petersen and Tilde geometries are considered, including the so-called Y-presentations for the Monster and related groups, and a complete indentification of Y-groups is given. This is an essential purchase for researchers into finite group theory, finite geometries and algebraic combinatorics.

    Reviews

    Review of the hardback:‘… this book is an essential purchase for researcher in finite group theory, finite geometries and algebraic combinatorics.’

    Anatoli Kondrat’ev Source: Zentralblatt für Mathematik

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