论文标题
图形覆盖物和（IM）原始同源性：一些异常低度的新示例
Graph coverings and (im)primitive homology: some new examples of exceptionally low degree
论文作者
论文摘要
给定图形的有限覆盖$ f：y \ to x $，并非总是如此，$ h_1（y; \ m m i; \ m m i; \ \ m m mathbb {c}）$跨越了$π_1（x）$的原始元素的升力。在本文中，我们研究了这种情况并非如此，我们在这里为此提供了最简单的已知封面示例，其属性的覆盖率高达128。我们的第一步是将注意力集中在特殊的图形封面上，其中甲板组是有限的$ p $ - 组。对于此类封面，有一个代表理论标准，用于识别存在属性的甲板组。我们提出了一种用于确定有限的$ p $ - 组是否满足仅使用组的字符表的算法。最后，我们提供了所有有限$ p $ - 等级$ \ geq 3 $和订单$ <1000 $的完整人口普查，满足了此标准，所有这些都是新示例。
Given a finite covering of graphs $f : Y \to X$, it is not always the case that $H_1(Y;\mathbb{C})$ is spanned by lifts of primitive elements of $π_1(X)$. In this paper, we study graphs for which this is not the case, and we give here the simplest known nontrivial examples of covers with this property, with covering degree as small as 128. Our first step is focusing our attention on the special class of graph covers where the deck group is a finite $p$-group. For such covers, there is a representation-theoretic criterion for identifying deck groups for which there exist covers with the property. We present an algorithm for determining if a finite $p$-group satisfies this criterion that uses only the character table of the group. Finally, we provide a complete census of all finite $p$-groups of rank $\geq 3$ and order $< 1000$ satisfying this criterion, all of which are new examples.
