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Enumeration of finite groups Cambridge Tracts in Mathematics Series Number 173 1st Edition by Simon Blackburn, Peter Neumann, Geetha Venkataraman 0521882176 9780521882170

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Enumeration of finite groups 1st Edition Simon R. Blackburn Digital Instant Download

Author(s): Simon R. Blackburn, Peter M. Neumann OBE, Geetha Venkataraman
ISBN(s): 9780521882170, 0521882176
Edition: 1
File Details: PDF, 1.34 MB
Year: 2007
Language: english
SKU: EB-882568 Category: Tags: , ,

Enumeration of finite groups Cambridge Tracts in Mathematics Series Number 173 1st Edition by Simon Blackburn, Peter Neumann, Geetha Venkataraman – Ebook PDF Instant Download/Delivery: 0521882176, 9780521882170

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Product details:

ISBN 10: 0521882176

ISBN 13: 9780521882170

Author: Simon R. Blackburn, Peter M. Neumann OBE, Geetha Venkataraman

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.

Enumeration of finite groups Cambridge Tracts in Mathematics Series Number 173 1st Table of contents:

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

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Tags: Simon Blackburn, Peter Neumann, Geetha Venkataraman, Enumeration