It takes the average reader 4 hours and 15 minutes to read The Solution of the k(Gv) Problem by Peter Schmid
Assuming a reading speed of 250 words per minute. Learn more
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 TheoryBlocks of Characters and Brauer's k(B) ProblemThe k(GV) ProblemSymplectic and Orthogonal ModulesReal VectorsReduced Pairs of Extraspecial TypeReduced Pairs of Quasisimple TypeModules Without Real VectorsClass Numbers of Permutation GroupsThe Final Stages of the ProofPossibilities for k(GV) = |V|Some Consequences for Block TheoryThe Non-Coprime Situation Readership: Postgraduate students and researchers with background and research interests in group and representation theory. Keywords:Conjugacy Classes;Characters;Blocks of Characters;k(B) Problem;Cohomology of Finite Groups;Schur Multiplier;Weil Characters;Atlas GroupsKey Features:First complete treatment of the k(GV) problem and its solutionPresentation of much new material and methods different from the available literatureSystematic use of Clifford theory, leading to extraspecial or quasisimple groupsStudy of holomorphs of extraspecial groups and of Weil charactersDevelopment of counting techniques for finding regular orbits or real vectorsReviews:Mathematical Reviews
The Solution of the k(Gv) Problem by Peter Schmid is 248 pages long, and a total of 63,984 words.
This makes it 84% the length of the average book. It also has 78% more words than the average book.
The average oral reading speed is 183 words per minute. This means it takes 5 hours and 49 minutes to read The Solution of the k(Gv) Problem aloud.
The Solution of the k(Gv) Problem is suitable for students ages 12 and up.
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