Finite Soluble Groups

This is our account of the theory of finite soluble groups as it has developed during the past 30 years. We have concentrated on those parts of the subject where a coherent and unified body of knowledge has emerged: the theory of Schunck classes and formations with their associated subgroups, the projectors and normalizers; the dual theory of Fitting classes with their injectors and radicals. All this material can be viewed as one vast and splendid generalization of the subgroups of Sylow and Hall; indeed, to have engendered an expansion of knowledge of such cosmic proportions, Sylow's theorem might well be compared to the Big Bang. Historical introductions to these themes can be found at the beginning of Chapters III and VIII. We have made no attempt to treat what is generally known as Hall-Higman theory and its manifold applications; only a separate monograph could hope to do justice to that.