## An Introduction to Groups: A Computer Illustrated TextAn Introduction to Groups: A Computer Illustrated Text discusses all the concepts necessary for a thorough understanding of group theory. The book covers various theorems, including Lagrange and Sylow. It also details Cayley tables, Burnside's lemma, homomorphisms, and dicyclic groups. The book is ideal for advanced mathematics students and beginning undergraduates. |

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### Contents

Introduction | 1 |

Groups | 14 |

Group Actions | 28 |

Conjugacy | 39 |

Homomorphisms and Quotient Groups | 51 |

Constructing Groups | 65 |

Program Notes | 79 |

List of Groups | 85 |

### Common terms and phrases

1-cycles action table associative law axioms belongs to H bracket notation Burnside's lemma calculations Cayley table chapter concept of conjugacy conjugacy classes Conjugate Subgroups consists contain cosets of H Create a Group cycle notation cycle structure cyclic group define denoted dicyclic groups dihedral groups direct products divide the order element g element of G element of order example expression finite group Fix(g g in G Gi/N group action group elements group G group of order group S4 homomorphism identity element identity permutation inverse isomorphism kernel Lagrange's theorem left cosets mapping menu normal subgroup odd permutations one-to-one Orb(x order 16 permutation group prime number program called prove quotient group Rename and Reorder right cosets rotations Run the program S3 x Z2 set of symbols square Stab(x subgroup H subgroup of G subgroup of order subset Suppose Sylow Theorem symmetries write Z4 x Z2