The Subgroup Structure of the Finite Classical Groups

In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results.

With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory.

1. Motivation and setting for the results; 2. Basic properties of the classical groups; 3. The statement of the main theorem; 4. The structure and conjugacy of the members of C; 5. Properties of the finite simple groups; 6. Non-maximal subgroups in C: the examples; 7. Determining the maximality of members of C, Part I; 8. Determining the maximality of members of C, Part II.

With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results.