The maximal subgroups of the low-dimensional finite classical groups / / John N. Bray, Derek F. Holt, Colva M. Roney-Dougal [[electronic resource]]

• Autore: Bray John N (John Nicholas)
• Pubblicazione: Cambridge : , : Cambridge University Press, , 2013
• Descrizione fisica: 1 online resource (xiv, 438 pages) : digital, PDF file(s)
• Disciplina: 512.23
• Soggetto topico: Finite groups; Finite groups - Mathematical models; Maximal subgroups; Maximal subgroups - Mathematical models
• Persona (resp. second.): HoltDerek F.; Roney-DougalColva Mary
• Note generali: Title from publisher's bibliographic system (viewed on 05 Oct 2015).
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Cover; Contents; Foreword by Martin Liebeck; Preface; 1 Introduction; 1.1 Background; 1.2 Notation; 1.3 Some basic group theory; 1.4 Finite fields and perfect fields; 1.5 Classical forms; 1.6 The classical groups and their orders; 1.7 Outer automorphisms of classical groups; 1.8 Representation theory; 1.9 Tensor products; 1.10 Small dimensions and exceptional isomorphisms; 1.11 Representations of simple groups; 1.12 The natural representations of the classical groups; 1.13 Some results from number theory; 2 The main theorem and the types of geometric subgroups; 2.1 The main theorem ; 2.2 Introducing the geometric types2.3 Preliminary arguments concerning maximality; 3 Geometric maximal subgroups; 3.1 Dimension 2; 3.2 Dimension 3; 3.3 Dimension 4; 3.4 Dimension 5; 3.5 Dimension 6; 3.6 Dimension 7; 3.7 Dimension 8; 3.8 Dimension 9; 3.9 Dimension 10; 3.10 Dimension 11; 3.11 Dimension 12; 4 Groups in Class S: cross characteristic; 4.1 Preamble; 4.2 Irrationalities; 4.3 Cross characteristic candidates; 4.4 The type of the form and the stabilisers in Ω and C; 4.5 Dimension up to 6: quasisimple and conformal groups; 4.6 Determining the effects of duality and field automorphisms ; 5.11 Summary of the S2*-maximals6 Containments involving S-subgroups; 6.1 Introduction; 6.2 Containments between S1- and S2*-maximal subgroups; 6.3 Containments between geometric and S*-maximal subgroups; 7 Maximal subgroups of exceptional groups; 7.1 Introduction; 7.2 The maximal subgroups of Sp4(2e) and extensions; 7.3 The maximal subgroups of Sz(q) and extensions; 7.4 The maximal subgroups of G2(2e) and extensions; 8 Tables; 8.1 Description of the tables; 8.2 The tables; References; Index of Definitions
• Sommario/riassunto: 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.
• Titolo autorizzato: The maximal subgroups of the low-dimensional finite classical groups
• ISBN: 1-139-89195-2; 1-107-27162-2; 1-107-27697-7; 1-107-27371-4; 1-107-27820-1; 1-107-27494-X; 1-139-19257-4; 1-107-27214-9
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910464311503321
• Lo trovi qui: Univ. Federico II
• Serie: London Mathematical Society lecture note series ; ; 407.