Solution Of The K(gv) Problem, The (Icp Advanced Texts In Mathematics 4)

Solution Of The K(gv) Problem, The (Icp Advanced Texts In Mathematics 4)

By: Peter Schmid (author)Hardback

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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.

Contents

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.

Product Details

  • ISBN13: 9781860949708
  • Format: Hardback
  • Number Of Pages: 248
  • ID: 9781860949708
  • ISBN10: 1860949703

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