Extensions of unipotent characters and the inductive McKay condition.
One of the main conjectures in the representation theory is the McKay conjecture: for every finite group \(G\) and every prime number \(p\) \[ |\text{Irr}_{p'}(G)|=|\text{Irr}_{p'}(N_G(P))|, \] where \(P\) is a Sylow \(p\)-subgroup of \(G\). The author has shown that the McKay conjecture is true if every finite simple group is good for every prime divisor of its order. In this paper it is proved an extendibility result for unipotent characters of groups of Lie type (Theorem 2.4) and it is finished the result that every group of Lie type is good for every prime \(p\geq 3\) different from the defining characteristic (Theorem 3.2).
numbers of complex irreducible characters
scientific article; zbMATH DE number 5376941
scientific article