finite classical groups over finite fields
The maximal subgroups of the low-dimensional finite classical groups.
This book classifies the maximal subgroups of all the finite classical groups of dimension 12 or less, it is also describes the maximal subgroups of the almost simple finite exceptional groups with socle one of \(Sz(q)\), \(G_2(q)\), \(^2G_2(q)\) or \(^3D_4(q)\). This work fills a long-standing gap in the literature. 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 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.
scientific article; zbMATH DE number 6237789