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.    Contents: Conjugacy Classes, Characters and Clifford Theory; Blocks of Characters and Brauer's k(B) Problem; The k(GV) Problem; Symplectic and Orthogonal Modules; Real Vectors; Reduced Pairs of Extraspecial Type; Reduced Pairs of Quasisimple Type; Modules Without Real Vectors; Class Numbers of Permutation Groups; The Final Stages of the Proof; Possibilities for k(GV) = |V | Some Consequences for Block Theory; The Non-Coprime Situation.

The Solution of the k(GV) Problem (ICP Advanced Texts in Mathematics) PDF

The list of books you might like