Cambridge University Press eBooks· 2013
The Maximal Subgroups of the Low-Dimensional Finite Classical Groups
- 542citations
- 2013year
Short summary
This book provides a comprehensive classification of maximal subgroups within low-dimensional finite classical and exceptional groups, presenting over 80 tables of previously unseen results.
AI-generated from the title and abstract; the full text is not read.
Key points
- Classifies maximal subgroups of finite classical groups (dim <= 12) and specific exceptional groups.
- Employs theoretical and computational tools, with downloadable Magma code.
- Contains over 80 tables detailing maximal subgroups, including previously unseen results.
- Provides insights into the structure and action of geometric and almost simple subgroups.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Cambridge University Press eBooks, 2013 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics