## A Characterization of SL(3,8) |

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### Contents

THE EXAMPLES | 9 |

THE BASIC STRUCTURE OF M | 14 |

A BASIC STRUCTURE THEOREM | 26 |

4 other sections not shown

### Common terms and phrases

2-closed 2-subgroup of G 64 and exponent abelian of order acts trivially Aut(B automorphism of order Burnside's Theorem CH(P Chapter character theory characteristic subgroup classes of elements classes of involutions CM(K CM(P conjugate contains a C(7)-subgroup contradicts the fact cosets Tx Cs(x cyclic group Definition 4.1 elementary abelian group elementary abelian subgroups elements of order fixed point free Frattini argument G is isomorphic G satisfies G-conjugate group G group of order group satisfying Hypotheses Hall subgroup HCM(P Hypotheses H hypotheses of Theorem involution in S-L irreducible characters isomorphic to SL(2,8 JD(S K-invariant subgroup Lemma is proved Let G matrices maximal 2-local subgroup minimal criminal minimal normal subgroup NG(A nilpotent NM(S normal 7-complement number of cosets Observe order 64 point free automorphism proper K-invariant subspaces satisfies the hypotheses semidirect product subgroup H subgroup of Definition subgroups of order Suzuki 2-group Sylow 2-subgroup T-classes Theorem 3.1 vector space