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ISBN: 0521413621 0521623499 9780521413626 9780521623490 Year: 1999 Volume: v. 76, 91 Publisher: Cambridge ; New York : Cambridge University Press,
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Book
ISBN: 1139881906 1107383706 1107394937 1299909159 0511953984 0511833121 1107390141 1107398568 0511525931 Year: 1999 Publisher: Cambridge : Cambridge University Press,
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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.
Sporadic groups (Mathematics) --- Groups, Sporadic (Mathematics) --- Finite groups
ISSN: 12723835 ISBN: 2856290736 9782856290736 Year: 1999 Volume: 7 Publisher: Paris : Société Mathématique de France - SMF,
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Riemann surfaces --- Teichmuller spaces --- Moduli theory --- Class groups (Mathematics) --- Quantum field theory --- Riemann, Surfaces de --- Teichmuller, Espaces de --- Modules, Théorie des --- Groupes de classes (Mathématiques) --- Champs, Théorie quantique des --- Analytic spaces --- Espaces analytiques --- Complex manifolds. --- Variétés complexes. --- Teichmüller, Espaces de --- Teichmüller spaces. --- Groupoïdes --- Groupoids --- Teichmüller, Espaces de --- Groupoïdes. --- Théorie quantique des champs --- Variétés complexes. --- Riemann surfaces - Congresses --- Teichmuller spaces - Congresses --- Moduli theory - Congresses --- Class groups (Mathematics) - Congresses --- Quantum field theory - Congresses
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