For a normal subgroup $K$ of a finite group $G$ and a $G$-invariant irreducible character $\xi$ of $K$ we show under a certain condition there is a bijection between the set of relative defect zero irreducible characters of $G$ lying over $\xi$ and the set of defect zero irreducible characters of $G/K$.
"Defect zero characters and relative defect zero characters." Proc. Japan Acad. Ser. A Math. Sci. 88 (9) 149 - 151, November 2012. https://doi.org/10.3792/pjaa.88.149