## Finite simple groups: proceedings of an instructional conference organized by the London Mathematical Society (a NATO Advanced Study Institute)Martin Beynon Powell, Graham Higman, London Mathematical Society |

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### Contents

Chapter | 1 |

Notation and Preliminary Results | 3 |

Alperins Theorem | 5 |

Copyright | |

50 other sections not shown

### Common terms and phrases

2-constrained arbitrary assume automorphism block Brauer CG(a CG(P character of G characteristic characteristic subgroup Chevalley groups commutative conjugacy class conjugate contains fusion controls strong fusion Corollary corresponding coset cyclic define definition denote dodecad elementary abelian 2-subgroup epimorphism exists finite group Frattini argument functor on G fusion in G Gorenstein group algebra group G group of order Hence homomorphism idempotent implies indecomposable induction integers involution irreducible characters isomorphic Lemma Let G Lie algebra linear groups main theorem Math maximal minimal normal subgroup module NG(P noncyclic nontrivial normal p-complement normal subgroup obtain octad odd order Op(G p-adic p-group p-stable p-Sylow permutation prime proof of Theorem Proposition prove representation ring root system section conjugacy functor section of G semi-simple signalizer functor theorem solvable Steinberg structure subgroup of G subset Suppose Sylow p-subgroup transitivity theorem unique vector space Weyl group Z(OG