Description |
1 online resource (160 pages) |
Series |
London Mathematical Society Student Texts, 77 ; v. 77 |
|
London Mathematical Society Student Texts, 77
|
Contents |
Cover; Title; Copyright; Contents; Preface; Editor's introduction; I An introduction to compact p-adic Lie groups; 1 Introduction; 2 From finite p-groups to compact p-adic Lie groups; 2.1 Nilpotent groups; 2.2 Finite p-groups; 2.3 Lie rings; 2.4 Applying Lie methods to groups; 2.5 Absolute values; 2.6 p-adic numbers; 2.7 p-adic integers; 2.8 Preview: p-adic analytic pro-p groups; 3 Basic notions and facts from point-set topology; 4 First series of exercises; 5 Powerful groups, profinite groups and pro-p groups; 5.1 Powerful finite p-groups; 5.2 Profinite groups as Galois groups |
|
5.3 Profinite groups as inverse limits5.4 Profinite groups as profinite completions; 5.5 Profinite groups as topological groups; 5.6 Pro-p groups; 5.7 Powerful pro-p groups; 5.8 Pro-p groups of finite rank -- summary ofcharacterisations; 6 Second series of exercises; 7 Uniformly powerful pro-p groups and Zp-Lie lattices; 7.1 Uniformly powerful pro-p groups; 7.2 Associated additive structure; 7.3 Associated Lie structure; 7.4 The Hausdorff formula; 7.5 Applying the Hausdorff formula; 8 The group GLd(Zp), just-infinite pro-p groups and the Lie correspondence for saturable pro-p groups |
|
8.1 The group GLd(Zp) -- an example8.2 Just-infinite pro-p groups; 8.3 Potent filtrations and saturable pro-p groups; 8.4 Lie correspondence; 9 Third series of exercises; 10 Representations of compact p-adic Lie groups; 10.1 Representation growth and Kirillov's orbit method; 10.2 The orbit method for saturable pro-p groups; 10.3 An application of the orbit method; References for Chapter I; II Strong approximation methods; 1 Introduction; 2 Algebraic groups; 2.1 The Zariski topology on Kn; 2.2 Linear algebraic groups as closed subgroups of GLn(K); Basic examples |
|
Basic properties of Algebraic groupsFields of definition and restriction of scalars; The Lie algebra of G; Connection with Lie algebras of locally compact topological groups; 2.3 Semisimple algebraic groups: the classification ofsimply connected algebraic groups over K; 2.4 Reductive groups; 2.5 Chevalley groups; 3 Arithmetic groups and the congruence topology; 3.1 Rings of algebraic integers in number fields; 3.2 The congruence topology on GLn(k) and GLn(O); Valuations of k; 3.3 Arithmetic groups; 4 The strong approximation theorem; 4.1 An aside: Serre's conjecture; 5 Lubotzky's alternative |
|
6 Applications of Lubotzky's alternative6.1 The finite simple groups of Lie type; 6.2 Refinements; 6.3 Normal subgroups of linear groups; 6.4 Representations, sieves and expanders; 7 The Nori -- Weisfeiler theorem; 7.1 Unipotently generated subgroups of algebraic groups over finite fields; 8 Exercises; References for Chapter II; III A newcomer's guideto zeta functions of groups and rings; 1 Introduction; 1.1 Zeta functions of groups; 1.2 Zeta functions of rings; 1.3 Linearisation; 1.4 Organisation of the chapter; 2 Local and global zeta functions; 2.1 Rationality and variation with the prime |
Summary |
An introduction to three key aspects of current research in infinite group theory, suitable for graduate students |
Notes |
2.2 Flag varieties and Coxeter groups |
Bibliography |
Includes bibliographical references and index |
Notes |
Print version record |
Subject |
Profinite groups.
|
|
Group theory.
|
|
MATHEMATICS -- Group Theory.
|
|
Teoría de grupos
|
|
Grupos profinitos
|
|
Group theory
|
|
Profinite groups
|
|
Gruppentheorie
|
|
Proendliche Gruppe
|
Form |
Electronic book
|
Author |
Nikolov, Nikolay
|
|
Voll, Christopher
|
|
Segal, Dan
|
ISBN |
9781139117593 |
|
1139117599 |
|
9781139128254 |
|
1139128256 |
|
9781139115421 |
|
1139115421 |
|
9780511793837 |
|
0511793839 |
|