Irreducible characters and normal subgroups in groups of odd order

Abstract

If b is a p-block of a normal subgroup N of a finite group G of odd order and b ⁎ is its Brauer correspondent in N N ( Q ) , where Q is a defect group of b, then for any p-block B of G over b, there exists a natural height-preserving bijection from the set of irreducible complex characters of B lying over height-zero characters onto the set of irreducible complex characters of the Harris–Knörr correspondent B ⁎ of B over b ⁎ lying over height-zero characters.