The solution of the k(GV) problem
著者
書誌事項
The solution of the k(GV) problem
（ICP advanced texts in mathematics / series editor, Dennis Barden, v. 4）
Imperial College Press, c2007
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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.
目次
- 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.
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