Solution Of The K(gv) Problem, The

Peter Schmid (Autor)

Buch | Hardcover

248 Seiten

2007
Imperial College Press (Verlag)
978-1-86094-970-8 (ISBN)

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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.

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.

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.

Reihe/Serie	Icp Advanced Texts In Mathematics ; 4
Verlagsort	London
Sprache	englisch
Themenwelt	Mathematik / Informatik ► Mathematik
ISBN-10	1-86094-970-3 / 1860949703
ISBN-13	978-1-86094-970-8 / 9781860949708
Zustand	Neuware