How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of how a group may be presented by generators and relations, a very little representation theory from the perspective of module theory, and a very little cohomology theory - but most of the basics are expounded here and the book is more or less…mehr
How many groups of order n are there? This is a natural question for anyone studying group theory, and this Tract provides an exhaustive and up-to-date account of research into this question spanning almost fifty years. The authors presuppose an undergraduate knowledge of group theory, up to and including Sylow's Theorems, a little knowledge of how a group may be presented by generators and relations, a very little representation theory from the perspective of module theory, and a very little cohomology theory - but most of the basics are expounded here and the book is more or less self-contained. Although it is principally devoted to a connected exposition of an agreeable theory, the book does also contain some material that has not hitherto been published. It is designed to be used as a graduate text but also as a handbook for established research workers in group theory.
Simon Blackburn is a Professor of Pure Mathematics at Royal Holloway, University of London. He is also currently Head of Department in Mathematics at Royal Holloway. His mathematical interests include group theory, combinatorics and cryptography and some of the connections between these areas.
Inhaltsangabe
1. Introduction Part I. Elementary Results: 2. Some basic observations Part II. Groups of Prime Power Order: 3. Preliminaries 4. Enumerating p-groups: a lower bound 5. Enumerating p-groups: upper bounds Part III. Pyber's Theorem: 6. Some more preliminaries 7. Group extensions and cohomology 8. Some representation theory 9. Primitive soluble linear groups 10. The orders of groups 11. Conjugacy classes of maximal soluble subgroups of symmetric groups 12. Enumeration of finite groups with abelian Sylow subgroups 13. Maximal soluble linear groups 14. Conjugacy classes of maximal soluble subgroups of the general linear group 15. Pyber's theorem: the soluble case 16. Pyber's theorem: the general case Part IV. Other Topics: 17. Enumeration within varieties of abelian groups 18. Enumeration within small varieties of A-groups 19. Enumeration within small varieties of p-groups 20. Miscellanea 21. Survey of other results 22. Some open problems Appendix A. Maximising two equations.
1. Introduction Part I. Elementary Results: 2. Some basic observations Part II. Groups of Prime Power Order: 3. Preliminaries 4. Enumerating p-groups: a lower bound 5. Enumerating p-groups: upper bounds Part III. Pyber's Theorem: 6. Some more preliminaries 7. Group extensions and cohomology 8. Some representation theory 9. Primitive soluble linear groups 10. The orders of groups 11. Conjugacy classes of maximal soluble subgroups of symmetric groups 12. Enumeration of finite groups with abelian Sylow subgroups 13. Maximal soluble linear groups 14. Conjugacy classes of maximal soluble subgroups of the general linear group 15. Pyber's theorem: the soluble case 16. Pyber's theorem: the general case Part IV. Other Topics: 17. Enumeration within varieties of abelian groups 18. Enumeration within small varieties of A-groups 19. Enumeration within small varieties of p-groups 20. Miscellanea 21. Survey of other results 22. Some open problems Appendix A. Maximising two equations.
Es gelten unsere Allgemeinen Geschäftsbedingungen: www.buecher.de/agb
Impressum
www.buecher.de ist ein Shop der buecher.de GmbH & Co. KG Bürgermeister-Wegele-Str. 12, 86167 Augsburg Amtsgericht Augsburg HRA 13309