Abstract:
Let $n\geqslant1$ be a given natural number. It is proved that a finite group $G$ has a $p$-block of defect $0$ if and only if for some $g\in G$ the number of solutions of the equation $g=[x_1,x_2]\dots[x_{2n-1},x_{2n}]$ is not divisible by $p$. A number of criteria for the existence of real characters of defect $0$ in $G$ is obtained.
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