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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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Enumeration of finite groups /
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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.
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https://doi.org/10.1017/CBO9780511542756
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