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Endliche Gruppen I

Endliche Gruppen I


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About the Book

Als ich im Jahre 1958 mit den Vorarbeiten zu diesem Buch begann, schien es noch moglich, eine einigermal3en vollstandige Darstellung der Strukturtheorie endlicher Gruppen in einem Bande zu geben. Die stiir- mische Entwicklung, welche die Theorie seitdem erlebt hat (das Literatur- verzeichnis gibt einen Eindruck davon), hat diese Zielsetzung unmoglich gemacht. Der vorliegende erste Band enthalt neben den Grundbegriffen die Theorie der nilpotenten, p-nilpotenten und auflosbaren Gruppen sowie die gewohnliche Darstellungstheorie. Da die Entwicklung der letzten Jahre nicht in diesen Gebieten ihren Schwerpunkthatte, konnte hier ein ziemlich vollstandiger Uberblick tiber den gegenwartigen Stand der Theorie gegeben werden. (Die in den allerletzten Jahren ent- standene Theorie der Formationen und Fittingklassen konnte nur noch zum Teil aufgenommen werden. ) Der zweite Band soIl die Theorie der subnormalen Untergruppen, die feinere Theorie der p-Lange, mehrfach transitive Permutationsgruppen und einige neuere Anwendungen der Charaktertheorie enthalten. Wegen der Ftille der Ergebnisse der letzten Jahre kann dabei keine Vollstandigkeit mehr angestrebt werden. Einige Teilgebiete wurden ausgeschlossen: 1. Eine einheitliche Behandlung der heute bekannten Serien von einfachen endlichen Gruppen nach der Methode von CHEVALLEY hatte umfangreiche Vorkenntnisse tiber Liesche Algebren erfordert. lch habe mich in Kap. II auf die projektiven und symplektischen Gruppen be- schrankt. Die einfachen Gruppen von MATHIEU und SUZUKI werden erst in Band 2 behandelt werden. 2. Die Theorie der p-Gruppen vom Exponenten p und die dazu benotigten Zusammenhange zwischen nilpotenten Gruppen und Lie- schen Ringen wurden nicht bertihrt.


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Product Details
  • ISBN-13: 9783642649820
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: Softcover reprint of the original 1st ed. 1967
  • Language: German
  • Returnable: Y
  • Spine Width: 41 mm
  • Width: 152 mm
  • ISBN-10: 3642649823
  • Publisher Date: 11 Nov 2011
  • Binding: Paperback
  • Height: 229 mm
  • No of Pages: 796
  • Series Title: Grundlehren Der Mathematischen Wissenschaften
  • Weight: 1115 gr


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