We prove that, given a finite graph Σ satisfying some mild conditions, there exist infinitely many tetravalent half-arc-transitive normal covers of Σ. Applying this result, we establish the existence of infinite families of finite tetravalent half-arc-transitive graphs with certain vertex stabilizers, and classify the vertex stabilizers up to order 2⁸ of finite connected tetravalent half-arc-transitive graphs. This sheds some new light on the longstanding problem of classifying the vertex stabilizers of finite tetravalent half-arc-transitive graphs.

中文翻译：

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构造无限多的四价图的半弧传递

我们证明，给定一个满足某些温和条件的有限图Σ，存在无限多个Σ的四价半弧传递正态覆盖。应用此结果，我们建立了带有某些顶点稳定器的无限四价半弧半透明图的无限族，并将顶点稳定器分类为有限连接的四价半弧半透明图的2 ⁸级。这为对有限四价半弧传递图的顶点稳定器进行分类的长期问题提供了新的思路。