论文标题
从示例到方法：两种案例来自整体组环中单位的研究
From examples to methods: Two cases from the study of units in integral group rings
论文作者
论文摘要
在本文中，我们回顾了卢萨尔·帕西（Luthar-Passi）和赫特维克（Hertweck）的第5和6级交替组的Zassenhaus猜想的第一个Zassenhaus猜想。我们描述了这些示例的研究如何导致两种方法的发展 - 帮助方法和晶格方法。我们展示这些方法并总结了使用它们实现的一些结果。然后，我们将这些方法应用于第7级交替组的第一个Zassenhaus猜想的研究，其中只有一个关键案例仍为全部答案开放。在示例中，我们在途中显示了如何将结果与提出的方法结合在一起，并收集开放问题，其中一些可以使用这些方法攻击。
In this article, we review the proofs of the first Zassenhaus Conjecture on conjugacy of torsion units in integral group rings for the alternating groups of degree 5 and 6, by Luthar-Passi and Hertweck. We describe how the study of these examples led to the development of two methods -- the HeLP method and the lattice method. We exhibit these methods and summarize some results which were achieved using them. We then apply these methods to the study of the first Zassenhaus conjecture for the alternating group of degree 7 where only one critical case remains open for a full answer. Along the way we show in examples how recently obtained results can be combined with the methods presented and collect open problems some of which could be attacked using these methods.
