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Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block (Springer Monographs in Mathematics) - Softcover
Synopsis
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.
"synopsis" may belong to another edition of this title.
Review
From the reviews:
"The author’s purpose here is to provide a better understanding of the subject, and to make the proofs understandable by students in group theory. The book, which is written in both Chinese (in simple characters) and English, consists of 16 sections. All the concepts are carefully introduced, and the proofs are complete and given in detail, assuming only knowledge of Wedderburn’s theorems, Nakayama’s Lemma and other basic algebraic topics." (Jian Bei An, Mathematical Reviews, 2003 j)
"The book ... contains an exposition of the author’s main result on the hyperfocal subalgebra of a block. ... The book is bilingual; each page consists of two columns, one with the Chinese and one with the English text. The author has made an effort to make his exposition self-contained ... . Also, the original proof of the main result has been modified and improved at several points. One of the new concepts that is studied ... is that of a divisor on a G-algebra." (Burkhard Külshammer, Zentralblatt MATH, Vol. 1002 (2), 2003)
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Blocks of Finite Groups. The Hyperfocal Subalgebra of a Block.
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Berlin, Heidelberg, Springer Berlin Heidelberg., 2002
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Blocks of Finite Groups (eng)
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Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block (Springer Monographs in Mathematics)
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Blocks of Finite Groups : The Hyperfocal Subalgebra of a Block
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Blocks of Finite Groups
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Springer Berlin Heidelberg Dez 2010, 2010
ISBN 10: 3642078028
ISBN 13: 9783642078026
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Taschenbuch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 224 pp. Chinesisch, Englisch. Seller Inventory # 9783642078026
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Blocks of Finite Groups
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ISBN 13: 9783642078026
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Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. The exceptional layout of this bilingual edition featurinmg two colums per page (one English, one Chinese) sharing the displayed mathematical formula, is the joint achievement of the author and A. Arabia.About 60 years ago, R. Brauer introduced bloc. Seller Inventory # 5046858
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Blocks of Finite Groups
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ISBN 10: 3642078028
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Taschenbuch. Condition: Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag KG, Sachsenplatz 4-6, 1201 Wien 224 pp. Englisch. Seller Inventory # 9783642078026
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Blocks of Finite Groups : The Hyperfocal Subalgebra of a Block
Published by
Springer Berlin Heidelberg, 2010
ISBN 10: 3642078028
ISBN 13: 9783642078026
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Taschenbuch
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Taschenbuch. Condition: Neu. Druck auf Anfrage Neuware - Printed after ordering - 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. Seller Inventory # 9783642078026