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Let $G$ be a finite group and let $p$ be a prime. Assume that there exists aprime $q$ dividing $|G|$ which does not divide the order of any $p$-localsubgroup of $G$. If $G$ is $p$-solvable or $q$ divides $p-1$, then $G$ has a$p$-block of defect zero. The case $q=2$ is a well-known result by Brauer andFowler.

Defect zero characters predicted by local structure