Enumeration of finite groups / Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman.

Format:

Book

Author/Creator:

Blackburn, Simon R., author.

Neumann, P. M., author.

Venkataraman, Geetha, author.

Series:

Cambridge tracts in mathematics ; 173.

Cambridge tracts in mathematics ; 173

Language:

English

Subjects (All):

Finite groups.

Physical Description:

1 online resource (xii, 281 pages) : digital, PDF file(s).

Edition:

1st ed.

Place of Publication:

Cambridge : Cambridge University Press, 2007.

Language Note:

English

Summary:

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.

Contents:

Some basic observations

Preliminaries

Enumerating p-groups: a lower bound

Enumerating p-groups: upper bounds

Some more preliminaries

Group extensions and cohomology

Some representation theory

Primitive soluble linear groups

The orders of groups

Conjugacy classes of maximal soluble subgroups of symmetric groups

Enumeration of finite groups with abelian Sylow subgroups

Maximal soluble linear groups

Conjugacy classes of maximal soluble subgroups of the general linear groups

Pyber's theorem: the soluble case

Pyber's theorem: the general case

Enumeration within varieties of abelian groups

Enumeration within small varieties of A-groups

Enumeration within small varieties of p-groups.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-18521-1

1-281-15366-4

9786611153663

1-139-13345-4

0-511-35537-8

0-511-35487-8

0-511-35429-0

0-511-54275-5

0-511-35589-0

OCLC:

190643124