The Maximal Subgroups of the Low-Dimensional Finite Classical Groups

Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.

This book classifies the maximal subgroups of finite classical groups in low dimension. It features previously unseen results and over 100 tables, making this an essential reference for researchers. It will appeal to graduate students as a textbook on finite simple groups, computational group theory (including Magma) and representation theory.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.