Description |
1 online resource (160 pages). |
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data file |
Series |
London Mathematical Society Student Texts, 77 ; v. 77
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London Mathematical Society student texts ; 77.
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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. |
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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. |
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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. |
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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. |
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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. |
Note |
2.2 Flag varieties and Coxeter groups. |
Summary |
An introduction to three key aspects of current research in infinite group theory, suitable for graduate students. |
Bibliography |
Includes bibliographical references and index. |
Local Note |
eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America |
Subject |
Profinite groups.
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Profinite groups. |
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Group theory.
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Group theory. |
Genre/Form |
Electronic books.
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Electronic book.
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Electronic books.
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Added Author |
Nikolov, Nikolay.
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Voll, Christopher.
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Segal, Daniel, 1947-
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Other Form: |
Print version: Klopsch, Benjamin. Lectures on Profinite Topics in Group Theory. Cambridge : Cambridge University Press, ©2011 9781107005297 |
ISBN |
9781139117593 |
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1139117599 |
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9781139128254 (electronic book) |
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1139128256 (electronic book) |
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9781139115421 |
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1139115421 |
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9780511793837 (electronic book) |
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0511793839 (electronic book) |
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9781107005297 |
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1107005299 |
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9780521183017 |
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0521183014 |
Standard No. |
9786613298577 |
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