## Methods of representation theory--with applications to finite groups and orders |

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### Contents

Algebraic Atheory | 1 |

Grothendieck groups of integral group rings | 44 |

40 Whitehead groups | 61 |

Copyright | |

43 other sections not shown

### Common terms and phrases

A-lattice A-module A(KG abelian arbitrary assume automorphism bijection block ideal block idempotent BN-pair central simple characters of G class group commutative diagram commutative ring completes the proof conjugacy class conjugate contains Corollary coset cyclic group D(ZG decomposition Dedekind domain defect group defined definition denote direct sum element exact sequence Exercise exists factor finite group follows formula Frobenius functor Frobenius module G-set given global field group G group of order hence homomorphism idele idempotent indecomposable modules induction injective integer irreducible characters isomorphism classes K-algebra kernel KG-module Lemma Let G Let H locally free matrix maximal ideal multiplication nonzero notation obtain p-adic p-block p-group parabolic subgroups permutation Picent prime primitive idempotent projective Proposition prove R-order remarks representation result RG-lattice semisimple simple modules split subgroups of G submodule subsection surjective Sylow p-subgroup Theorem theory trivial unique uniserial vector vertex Weyl group