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An introduction to three key aspects of current research in infinite group theory, suitable for graduate students.
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An introduction to three key aspects of current research in infinite group theory, suitable for graduate students.
Produktdetails
- Produktdetails
- London Mathematical Society St Nr.77
- Verlag: Cambridge University Press
- Seitenzahl: 158
- Erscheinungstermin: März 2011
- Englisch
- Abmessung: 231mm x 152mm x 15mm
- Gewicht: 363g
- ISBN-13: 9781107005297
- ISBN-10: 1107005299
- Artikelnr.: 32558966
- London Mathematical Society St Nr.77
- Verlag: Cambridge University Press
- Seitenzahl: 158
- Erscheinungstermin: März 2011
- Englisch
- Abmessung: 231mm x 152mm x 15mm
- Gewicht: 363g
- ISBN-13: 9781107005297
- ISBN-10: 1107005299
- Artikelnr.: 32558966
Preface; Editor's introduction; Part I. An Introduction to Compact p-adic Lie Groups: 1. Introduction; 2. From finite p-groups to compact p-adic Lie groups; 3. Basic notions and facts from point-set topology; 4. First series of exercises; 5. Powerful groups, profinite groups and pro-p groups; 6. Second series of exercises; 7. Uniformly powerful pro-p groups and Zp-Lie lattices; 8. The group GLd(Zp), just-infinite pro-p groups and the Lie correspondence for saturable pro-p groups; 9. Third series of exercises; 10. Representations of compact p-adic Lie groups; References for Part I; Part II. Strong Approximation Methods: 11. Introduction; 12. Algebraic groups; 13. Arithmetic groups and the congruence topology; 14. The strong approximation theorem; 15. Lubotzky's alternative; 16. Applications of Lubotzky's alternative; 17. The Nori-Weisfeiler theorem; 18. Exercises; References for Part II; Part III. A Newcomer's Guide to Zeta Functions of Groups and Rings: 19. Introduction; 20. Local and global zeta functions of groups and rings; 21. Variations on a theme; 22. Open problems and conjectures; 23. Exercises; References for Part III; Index.
Preface; Editor's introduction; Part I. An Introduction to Compact p-adic Lie Groups: 1. Introduction; 2. From finite p-groups to compact p-adic Lie groups; 3. Basic notions and facts from point-set topology; 4. First series of exercises; 5. Powerful groups, profinite groups and pro-p groups; 6. Second series of exercises; 7. Uniformly powerful pro-p groups and Zp-Lie lattices; 8. The group GLd(Zp), just-infinite pro-p groups and the Lie correspondence for saturable pro-p groups; 9. Third series of exercises; 10. Representations of compact p-adic Lie groups; References for Part I; Part II. Strong Approximation Methods: 11. Introduction; 12. Algebraic groups; 13. Arithmetic groups and the congruence topology; 14. The strong approximation theorem; 15. Lubotzky's alternative; 16. Applications of Lubotzky's alternative; 17. The Nori-Weisfeiler theorem; 18. Exercises; References for Part II; Part III. A Newcomer's Guide to Zeta Functions of Groups and Rings: 19. Introduction; 20. Local and global zeta functions of groups and rings; 21. Variations on a theme; 22. Open problems and conjectures; 23. Exercises; References for Part III; Index.