Description
Cambridge Lectures on Profinite Topics in Group Theory by Benjamin Klopsch, Nikolay Nikolov, Christopher Voll, Dan Segal
In This Book, Three Authors Introduce Readers To Strong Approximation Methods, Analytic Pro-P Groups And Zeta Functions Of Groups. Each Chapter Illustrates Connections Between Infinite Group Theory, Number Theory And Lie Theory. The First Introduces The Theory Of Compact P-Adic Lie Groups. The Second Explains How Methods From Linear Algebraic Groups Can Be Utilised To Study The Finite Images Of Linear Groups. The Final Chapter Provides An Overview Of Zeta Functions Associated To Groups And Rings. Derived From An Lms/Epsrc Short Course For Graduate Students, This Book Provides A Concise Introduction To A Very Active Research Area And Assumes Less Prior Knowledge Than Existing Monographs Or Original Research Articles. Accessible To Beginning Graduate Students In Group Theory, It Will Also Appeal To Researchers Interested In Infinite Group Theory And Its Interface With Lie Theory And Number Theory.
Table Of Contents : 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.