During the last 30 years the theory of finite groups has developed dramatically. Our understanding of finite simple groups has been enhanced by their classification. Many questions about arbitrary groups can be reduced to similar questions about simple groups and applications of the theory are beginning to appear in other branches of mathematics. The foundations of the theory of finite groups are developed in this book. Unifying themes include the Classification Theory and the classical linear groups. Lie theory appears in chapters on Coxeter groups, root systems, buildings and Tits systems. There is a new proof of the Solvable Signalizer Functor theorem and a brief outline of the proof of the Classification Theorem itself. For students familiar with basic abstract algebra this book will serve as a text for a course in finite group theory. Finite Group Theory provides the basic background necessary to understand the research literature and apply the theory. It will become the standard basic reference.
Table of Contents1. Preliminary results; 2. Permutation representations; 3. Representation of groups on groups; 4. Linear representations; 5. Permutation groups; 6. Extensions of groups and modules; 7. Spaces with forms; 8. p-groups; 9. Change of field of a linear representation; 10. Presentation of groups; 11. The generalized Fitting subgroup; 12. Linear representation of finite groups; 13. Transfer and fusion; 14. The geometry of groups of Lie type; 15. Signalizer functors; 16. Finite simple groups; References; List of symbols; Index.