The maximal subgroups of the low-dimensional finite classical groups.
type: Item
instance of: scholarly article
zbMATH Open document ID: 1303.20053
DOI: 10.1017/CBO9781139192576
author: Derek F. Holt
author: Colva M. Roney-Dougal
author: John N. Bray
publication date: 2013-12-12T00:00:00Z
Mathematics Subject Classification ID: 20G40
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20-02
Mathematics Subject Classification ID: 20D06
Mathematics Subject Classification ID: 20D25
Mathematics Subject Classification ID: 20-04
Mathematics Subject Classification ID: 68W30
zbMATH DE Number: 6237789
zbMATH Keywords: finite classical groups over finite fields
zbMATH Keywords: maximal subgroups
zbMATH Keywords: low-dimensional groups
zbMATH Keywords: finite simple groups
zbMATH Keywords: almost simple groups
describes a project that uses: Magma
MaRDI profile type: Publication
title: The maximal subgroups of the low-dimensional finite classical groups.
published in: London Mathematical Society Lecture Note Series
review text: 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.
reviewed by: Nan Ji-Zhu
description: scientific article; zbMATH DE number 6237789