In this paper, we provide a method to determine when transitive imprimitive groups synchronize a transformation of non-uniform kernel, that is, we give the condition of \(\langle G,\alpha \rangle\) being a synchronizing semigroup where G is transitive imprimitive and \(\alpha\) is transformation of non-uniform kernel.

中文翻译：

---

同步非均匀核变换的原始组

在本文中，我们提供了一种确定传递非本原群何时同步非均匀核变换的方法，即我们给出了\(\langle G,\alpha \rangle\)是一个同步半群的条件，其中G是传递非原语和\(\alpha\)是非均匀核的变换。