## A Course on Group TheoryAdvanced study focuses on finite groups and the idea of group actions. Chapters divided between normal and arithmetical structure of groups. 1978 edition. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

Some conventions and some basic facts | 1 |

Introduction to finite group theory | 6 |

Examples of groups and homomorphisms | 12 |

Normal subgroups homomorphisms and quotients | 36 |

Group actions on sets | 68 |

Finite pgroups and Sylows theorem | 88 |

Groups of even orders | 110 |

Series | 120 |

Direct products and the structure of finitely generated abelian groups | 163 |

Group actions on groups | 205 |

Transfer and splitting theorems | 232 |

Finite nilpotent and soluble groups | 266 |

295 | |

301 | |

306 | |

### Other editions - View all

### Common terms and phrases

action of G argue by induction Aut G CG(x characteristic subgroup composition series conjugacy class cyclic group defined definition denote direct product distinct primes element of G element of order factor of G finite group follows G acts G is finite G is nilpotent G is soluble G of order group G group of order H in G Hall subgroup Hence Hint homomorphism identity element infinite involution isomorphic Lemma Let G Let H maximal subgroup minimal normal subgroup Moreover nilpotent groups non-trivial finite normal in G notation p-group permutation positive integer prime divisor Proof proper subgroup prove quotient group series of G soluble group subgroup H subgroup of G subgroup of index subgroup of order subnormal in G subnormal subgroup Suppose that G Sylow p-subgroup Sylow's theorem transversal to H trivial unique vector space wreath product