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|a 9780511542756 (ebook)
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|a Blackburn, Simon R.,
|e author.
|0 http://id.loc.gov/authorities/names/nb2007026024
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1 |
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|a Enumeration of finite groups /
|c Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman.
|
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|a Cambridge :
|b Cambridge University Press,
|c 2007.
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|a 1 online resource (xii, 281 pages) :
|b digital, PDF file(s).
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|a Cambridge tracts in mathematics ;
|v 173
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|a Title from publisher's bibliographic system (viewed on 05 Oct 2015).
|
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|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.
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| 520 |
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|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.
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|a Finite groups.
|0 http://id.loc.gov/authorities/subjects/sh85048354
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|a Neumann, P. M.,
|e author.
|0 http://id.loc.gov/authorities/names/n86810008
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|a Venkataraman, Geetha,
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|a Blackburn, Simon R.
|t Enumeration of finite groups
|z 9780521882170.
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|v 173.
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