## Visual Group TheoryGroup theory is the branch of mathematics that studies symmetry, found in crystals, art, architecture, music and many other contexts, but its beauty is lost on students when it is taught in a technical style that is difficult to understand. Visual Group Theory assumes only a high school mathematics background and covers a typical undergraduate course in group theory from a thoroughly visual perspective. The more than 300 illustrations in Visual Group Theory bring groups, subgroups, homomorphisms, products, and quotients into clear view. Every topic and theorem is accompanied with a visual demonstration of its meaning and import, from the basics of groups and subgroups through advanced structural concepts such as semidirect products and Sylow theory. |

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### Contents

1 | |

3 | |

What do groups look like? | 11 |

Why study groups? | 25 |

Algebra at last | 41 |

Five families | 63 |

Subgroups | 97 |

Products and quotients | 117 |

Sylow theory | 193 |

Galois theory | 221 |

Answers to selected Exercises | 261 |

285 | |

287 | |

288 | |

About the Author | 297 |

Back cover | 298 |

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### Common terms and phrases

abelian groups action algebraic answer appears apply arrows begin called Cayley diagram Chapter column combining common complex compute configuration conjugate connect Consider contains copy corresponding create cube cycle cyclic groups Definition describe direct product divide domain elements equation example Exercise explain Explorer expression extension fact factor field Figure flip four Galois give given group theory groups of order homomorphism horizontal identity illustrated isomorphic lead left cosets Let‘s look mathematical means move multiplication table nodes numbers objects operation orbit original path pattern permutations polynomial possible prime proof prove puzzle question quotient rectangle represent requires result rewiring roots rotation Rule satisfies semidirect product shows solve step structure subgroup Sylow symmetry technique tell Theorem true turn vertical visual write