Solution Of The K(gv) Problem, The

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 proble...