Cohomology of Finite Groups:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1994
|
| Schriftenreihe: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
309 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | Some Historical Background This book deals with the cohomology of groups, particularly finite ones. His torically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homological algebra and algebraic K-theory. It arose primar ily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work of H. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the mean ings of the low dimensional homology groups of aspace X. For example, if the universal cover of X was three connected, it was known that H2(X;A) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describ ing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N |
| Beschreibung: | 1 Online-Ressource (VIII, 331 p) |
| ISBN: | 9783662062821 9783662062845 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-662-06282-1 |
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| 500 | |a Some Historical Background This book deals with the cohomology of groups, particularly finite ones. His torically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homological algebra and algebraic K-theory. It arose primar ily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work of H. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the mean ings of the low dimensional homology groups of aspace X. For example, if the universal cover of X was three connected, it was known that H2(X;A) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describ ing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N | ||
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Datensatz im Suchindex
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| author | Adem, Alejandro |
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| dewey-full | 514.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514.2 |
| dewey-sort | 3514.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-06282-1 |
| format | Electronic eBook |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662062821 9783662062845 |
| issn | 0072-7830 |
| language | English |
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| series2 | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics |
| spelling | Adem, Alejandro Verfasser aut Cohomology of Finite Groups by Alejandro Adem, R. James Milgram Berlin, Heidelberg Springer Berlin Heidelberg 1994 1 Online-Ressource (VIII, 331 p) txt rdacontent c rdamedia cr rdacarrier Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics 309 0072-7830 Some Historical Background This book deals with the cohomology of groups, particularly finite ones. His torically, the subject has been one of significant interaction between algebra and topology and has directly led to the creation of such important areas of mathematics as homological algebra and algebraic K-theory. It arose primar ily in the 1920's and 1930's independently in number theory and topology. In topology the main focus was on the work of H. Hopf, but B. Eckmann, S. Eilenberg, and S. MacLane (among others) made significant contributions. The main thrust of the early work here was to try to understand the mean ings of the low dimensional homology groups of aspace X. For example, if the universal cover of X was three connected, it was known that H2(X;A) depends only on the fundamental group of X. Group cohomology initially appeared to explain this dependence. In number theory, group cohomology arose as a natural device for describ ing the main theorems of class field theory and, in particular, for describing and analyzing the Brauer group of a field. It also arose naturally in the study of group extensions, N Mathematics Group theory K-theory Algebraic topology Algebraic Topology Group Theory and Generalizations K-Theory Mathematik Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Kohomologie (DE-588)4031700-6 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Kohomologie (DE-588)4031700-6 s 1\p DE-604 Milgram, R. James Sonstige oth https://doi.org/10.1007/978-3-662-06282-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Adem, Alejandro Cohomology of Finite Groups Mathematics Group theory K-theory Algebraic topology Algebraic Topology Group Theory and Generalizations K-Theory Mathematik Endliche Gruppe (DE-588)4014651-0 gnd Kohomologie (DE-588)4031700-6 gnd |
| subject_GND | (DE-588)4014651-0 (DE-588)4031700-6 |
| title | Cohomology of Finite Groups |
| title_auth | Cohomology of Finite Groups |
| title_exact_search | Cohomology of Finite Groups |
| title_full | Cohomology of Finite Groups by Alejandro Adem, R. James Milgram |
| title_fullStr | Cohomology of Finite Groups by Alejandro Adem, R. James Milgram |
| title_full_unstemmed | Cohomology of Finite Groups by Alejandro Adem, R. James Milgram |
| title_short | Cohomology of Finite Groups |
| title_sort | cohomology of finite groups |
| topic | Mathematics Group theory K-theory Algebraic topology Algebraic Topology Group Theory and Generalizations K-Theory Mathematik Endliche Gruppe (DE-588)4014651-0 gnd Kohomologie (DE-588)4031700-6 gnd |
| topic_facet | Mathematics Group theory K-theory Algebraic topology Algebraic Topology Group Theory and Generalizations K-Theory Mathematik Endliche Gruppe Kohomologie |
| url | https://doi.org/10.1007/978-3-662-06282-1 |
| work_keys_str_mv | AT ademalejandro cohomologyoffinitegroups AT milgramrjames cohomologyoffinitegroups |