THE SOLUTION OF THE K(GV) PROBLEM (V4)
| By: | Schmid Peter |
| Publisher: | World Scientific Publishing |
| Print ISBN: | 9781860949708 |
| eText ISBN: | 9781860949715 |
| Edition: | 0 |
| Format: | Page Fidelity |
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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.