## Finite Groups: A Second Course on Group TheoryThe theory of groups, especially of finite groups, is one of the most delightful areas of mathematics. Its proofs often have elegance and crystalline beauty. This textbook is intended for the reader who has been exposed to about three years of serious mathematics. The notion of a group appears widely in mathematics and even further afield in physics and chemistry, and the fundamental idea should be known to all mathematicians. In this textbook a purely algebraic approach is taken and the choice of material is based upon the notion of conjugacy. The aim is not only to cover basic material, but also to present group theory as a living, vibrant and growing discipline, by including references and discussion of some work up to the present day. |

### What people are saying - Write a review

User Review - Flag as inappropriate

group notes

### Contents

Introduction and Assumed Knowledge | 1 |

Series Soluble Groups and Nilpotent Groups | 7 |

Immediate Consequences of Sylows Theorems | 25 |

The SchurZassenhaus Theorem | 37 |

Finite Soluble Groups up to 1960 | 51 |

Fusion | 65 |

Composite Groups | 81 |

The Later Theory of Finite Soluble Groups | 89 |

### Other editions - View all

### Common terms and phrases

7r-group assume basis normalizers Carter subgroup central series CG(M Chap complement composition series conjugacy classes conjugate in G coprime covering subgroups definition denote direct product elements example Exercise finite group finite soluble group Fischer subgroup Fitting class Fitting subgroup G are conjugate G containing g G G g in G G is soluble Gaschiitz Gaschutz group G group of order group theory H of G Hall 7r-subgroup Hall subgroup Hence homomorphism of G Huppert induction injectors integer Lagrange's Theorem Let G Let H Math maximal 7r-subgroups maximal subgroup minimal normal subgroup modular law NG(P NG(Q nilpotent groups normal in G normal p-complement Np(Q Op(G p-group p-sylowizer proof Prove that G Second Isomorphism Theorem series of G set of primes subgroup H subgroup of G subnormal subgroups subset supersoluble Suppose G Sylow basis Sylow p-subgroup Sylow's Theorem transversal trivial X-injector of G