Enumeration of finite groups

著者

• Blackburn, Simon R.
• Neumann, P. M.
• Venkataraman, Geetha

書誌事項

Enumeration of finite groups

Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman

（Cambridge tracts in mathematics, 173）

Cambridge University Press, 2007

• : hbk.

注記

Includes bibliographical references and index

内容説明・目次

内容説明

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.

目次

• 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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詳細情報

• NII書誌ID(NCID): BA83624936
• ISBN:
  • 9780521882170
• 出版国コード: uk
• タイトル言語コード: eng
• 本文言語コード: eng
• 出版地: Cambridge
• ページ数/冊数: xii, 281 p.
• 大きさ: 24 cm
• 親書誌ID:
  • BA00134372