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The solution of the k(GV) problem

Author: Peter Schmid; Imperial College, London.
Publisher: London : Imperial College Press ; Singapore ; Hackensack, NJ : Distributed by World Scientific Pub., ©2007.
Series: Imperial College Press advanced texts in mathematics, v. 4.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
"The k(GV) conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product GV is bounded above by the order of V. Here V is a finite vector space and G a subgroup of GL(V) of order prime to that of V. It may be regarded as the special case of Brauer's celebrated k(B) problem dealing with p-blocks B of p-solvable groups (p a prime). Whereas Brauer's problem is still open in  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Peter Schmid; Imperial College, London.
ISBN: 9781860949708 1860949703
OCLC Number: 173368323
Description: xiv, 232 pages ; 24 cm.
Contents: Conjugacy Classes, Characters and Clifford Theory; Blocks of Characters and Brauer's k(B) Problem; Symplectic and Orthogonal Modules; Holomorphs of Extraspecial Groups and Weil Characters; Self-dual Modules and Real Vectors; Class Numbers of Permutation Groups; Counting Methods.
Series Title: Imperial College Press advanced texts in mathematics, v. 4.
Responsibility: Peter Schmid.
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Abstract:

The k(GV) problem has been finally solved, completing the work of a series of authors. This book describes the developments, ideas and methods, leading to this result.  Read more...

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Schmid has made an excellent job of providing an overall picture of what needs to be done to solve the k(GV) problem and developing enough of the necessary background results to provide Read more...

 
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   schema:reviewBody ""The k(GV) conjecture claims that the number of conjugacy classes (irreducible characters) of the semidirect product GV is bounded above by the order of V. Here V is a finite vector space and G a subgroup of GL(V) of order prime to that of V. It may be regarded as the special case of Brauer's celebrated k(B) problem dealing with p-blocks B of p-solvable groups (p a prime). Whereas Brauer's problem is still open in its generality, the k(GV) problem has recently been solved, completing the work of a series of authors over a period of more than forty years. In this book the developments, ideas and methods, leading to this remarkable result, are described in detail."--Jacket." ;
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