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. Sample Chapter(s). Chapter 1: Conjugacy Classes, Characters, and Clifford Theory (296 KB). 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. Readership: Postgraduate students and researchers with background and research interests in group and representation theory.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with The Solution of the K(GV) Problem. To get started finding The Solution of the K(GV) Problem, you are right to find our website which has a comprehensive collection of manuals listed. Our library is the biggest of these that have literally hundreds of thousands of different products represented.
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. Sample Chapter(s). Chapter 1: Conjugacy Classes, Characters, and Clifford Theory (296 KB). 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. Readership: Postgraduate students and researchers with background and research interests in group and representation theory.We have made it easy for you to find a PDF Ebooks without any digging. And by having access to our ebooks online or by storing it on your computer, you have convenient answers with The Solution of the K(GV) Problem. To get started finding The Solution of the K(GV) Problem, you are right to find our website which has a comprehensive collection of manuals listed. Our library is the biggest of these that have literally hundreds of thousands of different products represented.