John N. Bray

Maximal Subgroups of the Low-Dimensional Finite Classical Groups (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 25. Juli 2013
• Englisch
• ISBN-13: 9781107272866
• Artikelnr.: 39906872

Autorenporträt

John Bray obtained a PhD from the University of Birmingham in 1997, which was followed by postdoctoral positions at Birmingham and Queen Mary. He has held a lectureship at Queen Mary, University of London, since 2007. He is heavily involved with the online web-atlas of group representations, a popular resource in the group theory community.

Inhaltsangabe

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.