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The subgroup structure of the finite classical groups /
With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge ; New York :
Cambridge University Press,
1990.
|
| Colección: | London Mathematical Society lecture note series ;
129. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Kleidman, Peter. | |
| 245 | 1 | 4 | |a The subgroup structure of the finite classical groups / |c Peter Kleidman, Martin Liebeck. |
| 260 | |a Cambridge ; |a New York : |b Cambridge University Press, |c 1990. | ||
| 300 | |a 1 online resource (vii, 303 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
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| 490 | 1 | |a London Mathematical Society lecture note series ; |v 129 | |
| 504 | |a Includes bibliographical references (pages 289-295) and indexes. | ||
| 588 | 0 | |a Print version record. | |
| 520 | |a With the classification of the finite simple groups complete, much work has gone into the study of maximal subgroups of almost simple groups. In this volume the authors investigate the maximal subgroups of the finite classical groups and present research into these groups as well as proving many new results. In particular, the authors develop a unified treatment of the theory of the 'geometric subgroups' of the classical groups, introduced by Aschbacher, and they answer the questions of maximality and conjugacy and obtain the precise shapes of these groups. Both authors are experts in the field and the book will be of considerable value not only to group theorists, but also to combinatorialists and geometers interested in these techniques and results. Graduate students will find it a very readable introduction to the topic and it will bring them to the very forefront of research in group theory. | ||
| 505 | 0 | |a Cover -- Title -- Copyright -- Preface -- Standard notation and terminology -- Contents -- Chapter 1 Motivation and Setting for the Results -- 1.1 Introduction -- 1.2 The classical groups -- 1.3 The alternating, sporadic and exceptional groups -- Chapter 2 Basic Properties of the Classical Groups -- 2.1 Introduction -- 2.2 The linear groups -- 2.3 The unitary groups -- 2.4 The symplectic groups -- 2.5 The orthogonal groups -- 2.6 Orthogonal groups in odd dimension -- 2.7 Orthogonal groups with Witt defect 0. | |
| 505 | 8 | |a 2.8 Orthogonal groups with Witt defect 1 -- 2.9 Structure and isomorphisms -- 2.10 Classical groups acting on their associated geometries -- Chapter 3 The Statement of the Main Theorem -- 3.1 Introduction -- 3.2 How to determine the conjugacy amongst members of C -- 3.3 How to determine the structure of members of C -- 3.4 How to determine the overgroups of members of C -- 3.5 The tables -- Chapter 4 The Structure and Conjugacy of the Members of C -- 4.0 Introduction -- 4.1 The reducible subgroups C1 -- 4.2 The imprimitive subgroups C2. | |
| 505 | 8 | |a 4.3 The field extension subgroups C3 -- 4.4 The tensor product subgroups C4 -- 4.5 The subfield subgroups C5 -- 4.6 The symplectic-type subgroups C6 -- 4.7 The tensor product subgroups C7 -- 4.8 The classical subgroups C8 -- Chapter 5 Properties of the Finite Simple Groups -- 5.1 Basic properties of the simple groups -- 5.2 Subgroups of the simple groups -- 5.3 Representations of the simple groups -- 5.4 Groups of Lie type: representations in the natural characteristic -- 5.5 Further results on representations -- Chapter 6 Non-maximal Subgroups in C: the Examples. | |
| 546 | |a English. | ||
| 590 | |a eBooks on EBSCOhost |b EBSCO eBook Subscription Academic Collection - Worldwide | ||
| 650 | 0 | |a Group theory. | |
| 650 | 0 | |a Finite groups. | |
| 650 | 6 | |a Groupes finis. | |
| 650 | 6 | |a Théorie des groupes. | |
| 650 | 7 | |a MATHEMATICS |x Group Theory. |2 bisacsh | |
| 650 | 7 | |a Finite groups |2 fast | |
| 650 | 7 | |a Group theory |2 fast | |
| 650 | 7 | |a Groupes, théorie des. |2 ram | |
| 700 | 1 | |a Liebeck, M. W. |q (Martin W.), |d 1954- | |
| 776 | 0 | 8 | |i Print version: |a Kleidman, Peter. |t Subgroup structure of the finite classical groups. |d Cambridge ; New York : Cambridge University Press, 1990 |z 052135949X |w (DLC) 90176384 |w (OCoLC)21652322 |
| 830 | 0 | |a London Mathematical Society lecture note series ; |v 129. | |
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