Enumeration of finite 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 inc...
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2007
|
| Series: | Cambridge tracts in mathematics
173 |
| Subjects: | |
| Online Access: | BSB01 FHN01 UBR01 Volltext |
| 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 |
| Physical Description: | 1 Online-Ressource (xii, 281 Seiten) |
| ISBN: | 9780511542756 |
| DOI: | 10.1017/CBO9780511542756 |
Staff View
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| 505 | 8 | |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 | ||
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Record in the Search Index
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| author | Blackburn, Simon R. |
| author_GND | (DE-588)113768931 (DE-588)1019198230 |
| author_facet | Blackburn, Simon R. |
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| 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511542756 (OCoLC)850772801 (DE-599)BVBBV043941643 |
| dewey-full | 512.23 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512.23 |
| dewey-search | 512.23 |
| dewey-sort | 3512.23 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1017/CBO9780511542756 |
| format | Electronic eBook |
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| id | DE-604.BV043941643 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:39:16Z |
| institution | BVB |
| isbn | 9780511542756 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-029350613 |
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| owner_facet | DE-12 DE-92 DE-355 DE-BY-UBR |
| physical | 1 Online-Ressource (xii, 281 Seiten) |
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| publishDate | 2007 |
| publishDateSearch | 2007 |
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| publisher | Cambridge University Press |
| record_format | marc |
| series2 | Cambridge tracts in mathematics |
| spelling | Blackburn, Simon R. Verfasser (DE-588)113768931 aut Enumeration of finite groups Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman Cambridge Cambridge University Press 2007 1 Online-Ressource (xii, 281 Seiten) txt rdacontent c rdamedia cr rdacarrier Cambridge tracts in mathematics 173 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 Finite groups Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Abzählen (DE-588)4508960-7 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Abzählen (DE-588)4508960-7 s DE-604 Neumann, Peter M. 1940-2020 Sonstige (DE-588)1019198230 oth Venkataraman, Geetha Sonstige oth Erscheint auch als Druck-Ausgabe 978-0-521-88217-0 https://doi.org/10.1017/CBO9780511542756 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Blackburn, Simon R. Enumeration of finite groups 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 Finite groups Endliche Gruppe (DE-588)4014651-0 gnd Abzählen (DE-588)4508960-7 gnd |
| subject_GND | (DE-588)4014651-0 (DE-588)4508960-7 |
| title | Enumeration of finite groups |
| title_auth | Enumeration of finite groups |
| title_exact_search | Enumeration of finite groups |
| title_full | Enumeration of finite groups Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman |
| title_fullStr | Enumeration of finite groups Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman |
| title_full_unstemmed | Enumeration of finite groups Simon R. Blackburn, Peter M. Neumann, Geetha Venkataraman |
| title_short | Enumeration of finite groups |
| title_sort | enumeration of finite groups |
| topic | Finite groups Endliche Gruppe (DE-588)4014651-0 gnd Abzählen (DE-588)4508960-7 gnd |
| topic_facet | Finite groups Endliche Gruppe Abzählen |
| url | https://doi.org/10.1017/CBO9780511542756 |
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