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SOLUTION OF THE K(GV) PROBLEM, THE
Author(s): Peter Schmidt (Author)
- Publisher: Imperial College Press
- Publication Date: January 1, 2008
- Language: English
- Print length: 232 pages
- ISBN-10: 9781860949708
- ISBN-13: 9781860949708
Book Description
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.
Editorial Reviews
Review
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 self-contained proofs. -- Mathematical Reviews "Mathematical Reviews"
