Springer Monographs in Mathematics

Blocks of Finite Groups

The Hyperfocal Subalgebra of a Block

Authors: Puig, Lluis

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  • ISBN 978-3-662-11256-4
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About this book

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.

Reviews

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)


Table of contents (16 chapters)

Table of contents (16 chapters)

Buy this book

eBook $79.99
price for USA in USD
  • ISBN 978-3-662-11256-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
Softcover $99.99
price for USA in USD
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Bibliographic Information

Bibliographic Information
Book Title
Blocks of Finite Groups
Book Subtitle
The Hyperfocal Subalgebra of a Block
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2002
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-662-11256-4
DOI
10.1007/978-3-662-11256-4
Hardcover ISBN
978-3-540-43514-3
Softcover ISBN
978-3-642-07802-6
Series ISSN
1439-7382
Edition Number
1
Number of Pages
V, 215
Topics