On \(p\)-blocks of symmetric and alternating groups with all irreducible Brauer characters of prime power degree.
Let \(p\) be a prime, and let \(B\) be a \(p\)-block of a finite symmetric or alternating group of degree \(n\geq p\) with the property that the degrees of all irreducible Brauer characters in \(B\) are prime powers. The authors show that either \(n\leq 8\) and \(p\leq 5\), or \(B\) has defect zero. In the latter case, \(B\) corresponds to the partition \((n-1,1)\) or to the partition \((2,1^{n-2})\).
scientific article; zbMATH DE number 5365172
scientific article