## Mathieu groups |

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### Contents

INTRODUCTION | 1 |

HISTORICAL BACKGROUND AND CONSTRUCTION OF THE MATHIEU GROUPS | 11 |

LINEAR GROUPS | 24 |

14 other sections not shown

### Common terms and phrases

2-subgroup of M22 abelian of type alternating group automorphism group Burgoyne and Pong central involution classes of elements commutator subgroup computation conjugate classes Coxeter and Moser cyclic group cyclic of order denoted Dickson digits 22 dihedral group discussion element of class element of order elementary abelian subgroup factor group fixes the digits Fong Frattini subgroup Frobenius group Garbe and Mennicke given in Appendix group G group of order group on four izer Janko lattice of subgroups Let G linear group Mathieu group M22 maximal subgroup modulo Nagao non-abelian non-Sylow subgroups non-trivial normal subgroup normalizer order Order Description order eight order four order nine order sixteen order three Probenius 1904 self-centralizing simple group split extension Steiner systems subgroup is given subgroup of order SUBGROUPS CONTAINED Sylow 2-sub Sylow 2-subgroup symmetric group Theoremi Let two-fold transitive upper bound algorithm Whitelaw Witt writer has shown