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Enumeration of finite groups /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Enumeration of finite groups // Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman.
Author:	Blackburn, Simon R.,
other author:	Neumann, P. M.,
Description:	1 online resource (xii, 281 pages) :digital, PDF file(s). :
Notes:	Title from publisher's bibliographic system (viewed on 05 Oct 2015).
Subject:	Finite groups. -
Online resource:	https://doi.org/10.1017/CBO9780511542756
ISBN:	9780511542756 (ebook)

Enumeration of finite groups /
Blackburn, Simon R.,

Enumeration of finite groups /Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman. - 1 online resource (xii, 281 pages) :digital, PDF file(s). - Cambridge tracts in mathematics ;173. - Cambridge tracts in mathematics ;203..

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

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.

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.

ISBN: 9780511542756 (ebook)Subjects--Topical Terms:

684448
Finite groups.

LC Class. No.: QA177 / .B53 2007

Dewey Class. No.: 512.23

Enumeration of finite groups /
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245 1 0 $a Enumeration of finite groups / $c Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman.
264 1 $a Cambridge : $b Cambridge University Press, $c 2007.
300 $a 1 online resource (xii, 281 pages) : $b digital, PDF file(s).
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490 1 $a Cambridge tracts in mathematics ; $v 173
500 $a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
505 0 $a 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.
520 $a 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.
650 0 $a Finite groups. $3 684448
700 1 $a Neumann, P. M., $e author. $3 1441840
700 1 $a Venkataraman, Geetha, $e author. $3 1441841
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830 0 $a Cambridge tracts in mathematics ; $v 203. $3 1238301
856 4 0 $u https://doi.org/10.1017/CBO9780511542756