Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block / Edition 1

Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block / Edition 1

by Lluis Puig
Pub. Date:
Springer Berlin Heidelberg


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Blocks of Finite Groups: The Hyperfocal Subalgebra of a Block / Edition 1

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.

Product Details

ISBN-13: 9783540435143
Publisher: Springer Berlin Heidelberg
Publication date: 08/05/2002
Series: Springer Monographs in Mathematics
Edition description: 2002
Pages: 215
Product dimensions: 6.10(w) x 9.25(h) x 0.36(d)

Table of Contents

I. Introduction.- II. Lifting idempotents.- III. Points of the O-algebras and multiplicity of the points.- IV. Divisors on N-interior G-algebras.- V. Restriction and induction of divisors.- VI. Local pointed groups on N-interior G-algebras.- VII. On Green's indecomposability theorem.- VIII. Fusions in N-interior G-algebras.- IX. N-interior G-algebras through G-interior algebras.- X. The group algebra.- XI. Fusion Z-algebra of a block.- XII. Source algebras of blocks.- XIII. Local structure of the hyperfocal subalgebra.- XIV. Uniqueness of the hyperfocal subalgebra.- XV. Existence of the hyperfocal subalgebra.- XVI. On the exponential and logarithmic functions in O-algebras.

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