| Preface | |
| Notes for the reader | |
| Prerequisites--general group theory | |
| Groups and subgroups--the rudiments | p. 1 |
| Groups and homomorphisms | p. 5 |
| Series | p. 7 |
| Direct and semidirect products | p. 9 |
| G-sets and permutation representations | p. 17 |
| Sylow subgroups | p. 21 |
| Commutators | p. 22 |
| Finite nilpotent groups | p. 25 |
| The Frattini subgroup | p. 30 |
| Soluble groups | p. 34 |
| Theorems of Gaschutz, Schur-Zassenhaus, and Maschke | p. 38 |
| Coprime operator groups | p. 41 |
| Automorphism groups induced on chief factors | p. 44 |
| Subnormal subgroups | p. 47 |
| Primitive finite groups | p. 52 |
| Maximal subgroups of soluble groups | p. 57 |
| The transfer | p. 60 |
| The wreath product | p. 62 |
| Subdirect and central products | p. 73 |
| Extraspecial p-groups and their automorphism groups | p. 77 |
| Automorphisms of abelian groups | p. 83 |
| Prerequisites--representation theory | |
| Tensor products | p. 90 |
| Projective and injective modules | p. 95 |
| Modules and representations of K-algebras | p. 101 |
| The structure of a group algebra | p. 111 |
| Changing the field of a representation | p. 120 |
| Induced modules | p. 129 |
| Clifford's theorems | p. 139 |
| Homogeneous modules | p. 153 |
| Representations of abelian and extraspecial groups | p. 157 |
| Faithful and simple modules | p. 172 |
| Modules with special properties | p. 182 |
| Group constructions using modules | p. 190 |
| Introduction to soluble groups | |
| Preparations for the [actual symbols not reproducible]-theorem of Burnside | p. 204 |
| The proof of Burnside's [actual symbols not reproducible]-theorem | p. 210 |
| Hall subgroups | p. 216 |
| Hall systems of a finite soluble group | p. 220 |
| System normalizers | p. 235 |
| Pronormal subgroups | p. 241 |
| Normally embedded subgroups | p. 250 |
| Classes of groups and closure operations | |
| Classes of groups and closure operations | p. 262 |
| Some special classes defined by closure properties | p. 271 |
| Projectors and Schunck classes | |
| A historical introduction | p. 279 |
| Schunck classes and boundaries | p. 282 |
| Projectors and covering subgroups | p. 288 |
| Examples | p. 302 |
| Locally-defined Schunck classes and other constructions | p. 321 |
| Projectors in subgroups | p. 328 |
| The theory of formations | |
| Examples and basic results | p. 333 |
| Connections between Schunck classes and formations | p. 344 |
| Local formations | p. 356 |
| The theorem of Lubeseder and the theorem of Baer | p. 366 |
| Projectors and local formations | p. 375 |
| Theorems about f-hypercentral action | p. 386 |
| Normalizers | |
| Normalizers in general | p. 394 |
| Normalizers associated with a formation function | p. 396 |
| F-normalizers | p. 400 |
| Connections between normalizers and projectors | p. 408 |
| Precursive subgroups | p. 414 |
| Further theory of Schunck classes | |
| Strong containment and the lattice of Schunck classes | p. 426 |
| Complementation in the lattice | p. 440 |
| D-classes | p. 453 |
| Schunck classes with normally embedded projectors | p. 461 |
| Schunck classes with permutable and CAP projectors | p. 471 |
| Further theory of formations | |
| The formation generated by a single group | p. 479 |
| Supersoluble groups and chief factor rank | p. 483 |
| Primitive saturated formations | p. 497 |
| The saturation of a formation | p. 502 |
| Strong containment for saturated formations | p. 509 |
| Extreme classes | p. 516 |
| Saturated formations with the cover-avoidance property | p. 528 |
| Injectors and Fitting sets | |
| Historical introduction | p. 535 |
| Injectors and Fitting sets | p. 537 |
| Normally embedded subgroups are injectors | p. 548 |
| Fischer sets and Fischer subgroups | p. 554 |
| Fitting classes--examples and properties related to injectors | |
| Fundamental facts | p. 563 |
| Constructions and examples | p. 574 |
| Fischer classes, normally embedded, and permutable Fitting classes | p. 600 |
| Dominance and some characterizations of injectors | p. 617 |
| Dark's construction--the theme | p. 630 |
| Dark's construction--variations | p. 647 |
| Fitting classes--the Lockett section | |
| The definition and basic properties of the Lockett section | p. 677 |
| Fitting classes and wreath products | p. 697 |
| Normal Fitting classes | p. 704 |
| The Lausch group | p. 720 |
| Examples of Fitting pairs and Berger's theorem | p. 737 |
| The Lockett conjecture | p. 761 |
| Fitting classes--their behaviour as classes of groups | |
| Fitting formations | p. 775 |
| Metanilpotent Fitting classes with additional closure properties | p. 783 |
| Further theory of metanilpotent Fitting classes | p. 799 |
| Fitting class boundaries I | p. 806 |
| Fitting class boundaries II | p. 816 |
| Frattini duals and Fitting classes | p. 824 |
| Appendix [alpha]. A theorem of Oates and Powell | p. 833 |
| Appendix [beta]. Frattini extensions | p. 846 |
| Bibliography | p. 855 |
| List of Symbols | p. 871 |
| Index of Subjects | p. 873 |
| Index of Names | p. 889 |
| Table of Contents provided by Blackwell. All Rights Reserved. |
