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Lecture Notes for MTH 912 - Group Theory I with Meierfrankenfeld at Michigan State (MSU)

Notes Information

Material Type:Class Note
Professor:Meierfrankenfeld
Class:MTH 912 - Group Theory I
Subject:Mathematics
University:Michigan State University
Term:Spring 2007
Keywords:
  • Immediately
  • The Independent
  • Representations
  • Equal Numbers
  • Contradicting
  • Definitions
  • Interesting
  • Contradiction
  • Permutation
  • Isomorphism
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Group Theory Lecture Notes for MTH 912/913 04/05 Ulrich Meierfrankenfeld April 26, 2007 2 Contents 1 Group Theory 5 1.1 Group Action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2 Balanced Products of G-sets . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.3 Central by finite groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 1.4 Finite p-Groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 1.5 A p-complement Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2 General Representation Theory 21 2.1 Basic Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2 Krull-Schmidt Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 2.3 Maschke's Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.4 Jacobson Radical . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 2.5 Simple modules for algebras . . . . . . . . . . . ...

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