Dade's projective conjecture for \(p\)-solvable groups
Dade's conjecture relates the number of irreducible characters of fixed defect in a \(p\)-block \(B\) of a finite group \(G\) to similar numbers in Brauer correspondents of \(B\) in \(p\)-local subgroups of \(G\). In the paper under review, the author proves the projective form of this conjecture for the class of \(p\)-solvable groups. More generally, he shows that in a minimal counterexample (if it exists) to this form of the conjecture every \(p\)-solvable normal subgroup is central. (Dade himself had indicated the possibility that his conjectures ultimately reduce to simple groups.)
scientific article; zbMATH DE number 1496011