## Representations of finite groups |

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### Contents

Algebras and Their Representations | 101 |

Representations of Groups | 167 |

Indecomposable Modules | 259 |

Copyright | |

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4-submodules A-module absolutely irreducible Artinian ring assume assumption bijection Bl(G Brauer character called central simple CG(x Chapter Cl(G commutative completely reducible conjugate class Corollary denote dimK direct sum discrete valuation division ring element epimorphism equivalent exact sequence Exercise exists factor set finite following holds following statements hold following theorem Frobenius algebra group ring hence homomorphism idempotent idempotent decomposition indecomposable component indecomposable decomposition indecomposable modules induces injective integer Irr(G irreducible constituent irreducible representation isomorphism K-algebra K-basis Lemma Let G Let H linear main theorem matrix maximal monomorphism nilpotent Noetherian nonzero notation p-group p-subgroup of G prime ideal primitive idempotent principal indecomposable projective representation Proof representation module representation of G right ideal satisfying semisimple set of representatives simple algebra splitting field subgroup submodule suffices to show Suppose Theorem unique valuation ring whence x e G x e Irr(B