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Gruppentheorie by Wilhelm Specht

Gruppentheorie

by Wilhelm Specht
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Book cover type: Paperback
  • ISBN13: 9783642946684
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Publication Date:
  • Pages: 458
  • Original Price: EUR 56.07
  • Language: German
  • Edition: Softcover Repri
  • Item Weight: 649 grams
  • BISAC Subject(s): General

Der Begriff der Gruppe ist so alt wie die Mathematik selbst. Ins mathematische BewuBtsein tritt er jedoch erst mit Beginn des 19. Jahr- hunderts. Die Erfordernisse der GALOIsschen Theorie algebraischer Gleichungen fUhrten zu der Entwicklung einer Theorie der endlichen Permutationsgruppen, die sich im Verlaufe eines Jahrhunderts zu einer weitgespannten Theorie der Gruppen endlicher Ordnung umbildete. 1m gleichen Zeitraum gab aber auch die invariantentheoretische Ent- wicklungstendenz der Geometrie und der Analysis AnlaB zur Unter- suchung spezieller unendlicher Gruppen und fiihrte damit zu einem weiteren Ausbau der Gruppentheorie. Umgekehrt bot die Entwicklung dieser Theorie die Moglichkeit neuer Methoden in fast allen Teilgebieten der Mathematik. Aus diesem Wechselspiel gegenseitiger Anregungen entstand urn 1920 zugleich mit der vollstandigen Strukturumwandlung der Algebra und dem Eingang mengentheoretischer Dbeilegungen in die Mathematik die selbstandige Disziplin einer allgemeinen Gruppentheorie. Von den Ergebnissen der allgemeinen Gruppentheorie handelt dieses Buch. Dabei Vollstandigkeit anzustreben, wiirde alle Kraft iibersteigen und jeden Rahmen sprengen. Es kann nur Aufgabe sein, aus der riesen- haften Fiille der Ergebnisse eine Auswahl zu treffen, die den Leser die SchOnheit der Disziplin und die Vielfalt ihrer Methode erkennen laBt. Eine strenge Auswahl des Stoffes ist indes notwendig Funktion des personlichen Geschmacks; diese Feststellung muB den Kenner dariiber trosten, wenn er dies oder jenes vermiBt, was ihm am Herzen liegt. Die Enge des Raumes zwang zu konzisem Stil; ein genaues Sachver- zeichnis gibt dem Leser die erforderliche Hilfe.

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