The maximal subgroups of the low-dimensional finite classical groups /John N. Bray, Derek F. Holt, Colva M. Roney-Dougal.
Bray, John N.
The maximal subgroups of the low-dimensional finite classical groups /John N. Bray, Derek F. Holt, Colva M. Roney-Dougal. - Cambridge : Cambridge University Press, (c)2013. - 1 online resource. - London Mathematical Society lecture note series ; 407 .
Includes bibliographies and index.
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. 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.
Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.
9781139192576 9781461944799 9781107274945 9781107272149
016415941 Uk
Finite groups.
Maximal subgroups.
Electronic Books.
QA177 / .M395 2013
The maximal subgroups of the low-dimensional finite classical groups /John N. Bray, Derek F. Holt, Colva M. Roney-Dougal. - Cambridge : Cambridge University Press, (c)2013. - 1 online resource. - London Mathematical Society lecture note series ; 407 .
Includes bibliographies and index.
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. 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.
Classifies the maximal subgroups of the finite groups of Lie type up to dimension 12, using theoretical and computational methods.
9781139192576 9781461944799 9781107274945 9781107272149
016415941 Uk
Finite groups.
Maximal subgroups.
Electronic Books.
QA177 / .M395 2013