## Finite Groups Æ72: Proceedings of the Gainesville Conference on Finite Groups, March 23-24, 1972Finite Groups Æ72 |

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### Contents

1 | |

3 | |

6 | |

Chapter 4 Finite Groups Generated by Odd Transposition | 8 |

Chapter 5 Groups Generated by a Class of Elements of Order | 12 |

Chapter 6 Solvable Groups Automorphism Groups and Representation Theory | 19 |

Chapter 7 Groups Whose Sylow 2Groups Have Cyclic Commutator Groups | 25 |

Chapter 8 A Construction for the Smallest Fischer Group F 22 | 27 |

Chapter 16 Simple Groups of Conjugate Type Rank 5 | 84 |

Chapter 17 A Class of Simple Groups of Characteristic 2 | 98 |

Chapter 18 2Groups Which Contain Exactly Three Involutions | 101 |

Chapter 19 On Solving the Degree Equations in πGroups | 108 |

Chapter 20 On Finite Linear Groups of Degree Less Than q 1 2 | 116 |

Chapter 21 A Setting for the Leech Lattice | 117 |

Chapter 22 The Normal Structure of the OnePoint Stabilizer of a Doubly Transitive Group | 119 |

Chapter 23 FlagTransitive Subgroups of Chevalley Groups | 122 |

Chapter 9 Groups With a BNPair of Rank 2 | 36 |

Chapter 10 Characters of Symplectic Groups Over F2 | 41 |

Chapter 11 Strongly Closed Abelian 2Subgroups of Finite Groups | 55 |

Chapter 12 Finite Groups of Sectional 2Rank At Most 4 | 57 |

Chapter 13 Automorphisms of Extra Special Groups and Nonvanishing Degree 2 Cohomology | 68 |

Chapter 14 Characterizations of Some Finite Simple Chevalley Groups by Centralizers of Involution | 74 |

Chapter 15 Remark on Shults Graph Extension Theorem | 80 |

Chapter 24 Corollaries of Strongly Embedded Type from a A Theorem of Aschbacher | 126 |

Chapter 25 On Fusion in 2Sylow Intersections | 131 |

Chapter 26 The Existence and Uniqueness of Lyons Group | 138 |

Chapter 27 Isometries in Finite Groups of Lie Type | 142 |

Chapter 28 Centralizers of Involutions and the Classification Problem | 147 |

Chapter 29 A Characterization of Orthogonal Simple Groups PΩ2nq | 156 |

### Common terms and phrases

2-constrained 2-group 2-transitive A-components abelian Algebra appear assume automorphism group basic transpositions central involution character of level characterization characters of odd Chevalley group Chevalley type commutes conjugacy class contain exactly COROLLARY cyclic defined denote dihedral element of G elementary abelian exactly 3 involutions extension finite group finite simple group Fitting subgroup fusion G contains G is isomorphic group G group of Chevalley group of order group of sectional Harada hexad Higman hypothesis induction involution isomorphic jklmn Leech lattice lemma Let G Main Theorem Math maximal N)-pair nilpotent nontrivial normal subgroup odd order orbit orthogonal groups pair parabolic subgroup permutation prime problem proof of Theorem proper subgroups q odd quasisimple result sectional 2-rank Shult solvable group strongly embedded subgroup of G subgroup of index subgroup of order Sylow 2-subgroup symbols synthemes Weyl group