A restriction for singularities on collapsing orbifolds

An orbifold $X$ is locally homeomorphic to $G_x\mathrm{\backslash }{B}_r(0)$, where $G_x$ is a finite group acting on $B_r(0)\subset {\mathbb{R}}^n$, so that $G_x(0)=0$. For collapsing orbifolds with isolated singularities, we show there is a uniform bound in $\mathrm{\mid }{G}_x\mathrm{\mid }$.