Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2002
|
| Schriftenreihe: | Springer Monographs in Mathematics
|
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzero characteristic p: any indecomposable two-sided ideal that also is a direct summand of kG determines a G-block. But the main discovery of Brauer is perhaps the existence of families of infinitely many nonisomorphic groups having a "common block"; i.e., blocks having mutually isomorphic "source algebras". In this book, based on a course given by the author at Wuhan University in 1999, all the concepts mentioned are introduced, and all the proofs are developed completely. Its main purpose is the proof of the existence and the uniqueness of the "hyperfocal subalgebra" in the source algebra. This result seems fundamental in block theory; for instance, the structure of the source algebra of a nilpotent block, an important fact in block theory, can be obtained as a corollary. The exceptional layout of this bilingual edition featuring 2 columns per page (one English, one Chinese) sharing the displayed mathematical formulas is the joint achievement of the author and A. Arabia |
| Beschreibung: | 1 Online-Ressource (V, 215 p) |
| ISBN: | 9783662112564 9783642078026 |
| ISSN: | 1439-7382 |
| DOI: | 10.1007/978-3-662-11256-4 |
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Datensatz im Suchindex
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
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| dewey-sort | 3512.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-662-11256-4 |
| format | Electronic eBook |
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| id | DE-604.BV042423449 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:13Z |
| institution | BVB |
| isbn | 9783662112564 9783642078026 |
| issn | 1439-7382 |
| language | English |
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| physical | 1 Online-Ressource (V, 215 p) |
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| publishDate | 2002 |
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| publisher | Springer Berlin Heidelberg |
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| series2 | Springer Monographs in Mathematics |
| spelling | Puig, Lluís Verfasser aut Blocks of Finite Groups The Hyperfocal Subalgebra of a Block by Lluís Puig Berlin, Heidelberg Springer Berlin Heidelberg 2002 1 Online-Ressource (V, 215 p) txt rdacontent c rdamedia cr rdacarrier Springer Monographs in Mathematics 1439-7382 About 60 years ago, R. Brauer introduced "block theory"; his purpose was to study the group algebra kG of a finite group G over a field k of nonzero characteristic p: any indecomposable two-sided ideal that also is a direct summand of kG determines a G-block. But the main discovery of Brauer is perhaps the existence of families of infinitely many nonisomorphic groups having a "common block"; i.e., blocks having mutually isomorphic "source algebras". In this book, based on a course given by the author at Wuhan University in 1999, all the concepts mentioned are introduced, and all the proofs are developed completely. Its main purpose is the proof of the existence and the uniqueness of the "hyperfocal subalgebra" in the source algebra. This result seems fundamental in block theory; for instance, the structure of the source algebra of a nilpotent block, an important fact in block theory, can be obtained as a corollary. The exceptional layout of this bilingual edition featuring 2 columns per page (one English, one Chinese) sharing the displayed mathematical formulas is the joint achievement of the author and A. Arabia Mathematics Group theory Group Theory and Generalizations Mathematik Block Mathematik (DE-588)4146017-0 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 gnd rswk-swf Endliche Gruppe (DE-588)4014651-0 s Block Mathematik (DE-588)4146017-0 s 1\p DE-604 https://doi.org/10.1007/978-3-662-11256-4 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Puig, Lluís Blocks of Finite Groups The Hyperfocal Subalgebra of a Block Mathematics Group theory Group Theory and Generalizations Mathematik Block Mathematik (DE-588)4146017-0 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| subject_GND | (DE-588)4146017-0 (DE-588)4014651-0 |
| title | Blocks of Finite Groups The Hyperfocal Subalgebra of a Block |
| title_auth | Blocks of Finite Groups The Hyperfocal Subalgebra of a Block |
| title_exact_search | Blocks of Finite Groups The Hyperfocal Subalgebra of a Block |
| title_full | Blocks of Finite Groups The Hyperfocal Subalgebra of a Block by Lluís Puig |
| title_fullStr | Blocks of Finite Groups The Hyperfocal Subalgebra of a Block by Lluís Puig |
| title_full_unstemmed | Blocks of Finite Groups The Hyperfocal Subalgebra of a Block by Lluís Puig |
| title_short | Blocks of Finite Groups |
| title_sort | blocks of finite groups the hyperfocal subalgebra of a block |
| title_sub | The Hyperfocal Subalgebra of a Block |
| topic | Mathematics Group theory Group Theory and Generalizations Mathematik Block Mathematik (DE-588)4146017-0 gnd Endliche Gruppe (DE-588)4014651-0 gnd |
| topic_facet | Mathematics Group theory Group Theory and Generalizations Mathematik Block Mathematik Endliche Gruppe |
| url | https://doi.org/10.1007/978-3-662-11256-4 |
| work_keys_str_mv | AT puiglluis blocksoffinitegroupsthehyperfocalsubalgebraofablock |