The maximal subgroups of the low-dimensional finite classical groups
著者
書誌事項
The maximal subgroups of the low-dimensional finite classical groups
（London Mathematical Society lecture note series, 407）
Cambridge University Press, 2013
- : pbk
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注記
Includes bibliographical references (p. 429-434) and index
内容説明・目次
内容説明
This book classifies the maximal subgroups of the almost simple finite classical groups in dimension up to 12; it also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of Sz(q), G2(q), 2G2(q) or 3D4(q). Theoretical and computational tools are used throughout, with downloadable Magma code provided. The exposition contains a wealth of information on the structure and action of the geometric subgroups of classical groups, but the reader will also encounter methods for analysing the structure and maximality of almost simple subgroups of almost simple groups. Additionally, this book contains detailed information on using Magma to calculate with representations over number fields and finite fields. Featured within are previously unseen results and over 80 tables describing the maximal subgroups, making this volume an essential reference for researchers. It also functions as a graduate-level textbook on finite simple groups, computational group theory and representation theory.
目次
- Preface
- 1. Introduction
- 2. The main theorem, and types of geometric subgroups
- 3. Geometric maximal subgroups
- 4. Groups in class S: cross characteristic
- 5. Groups in Class S: defining characteristic
- 6. Containments involving S-subgroups
- 7. Maximal subgroups of exceptional groups
- 8. Tables.
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