论文标题
小$ \ mathfrak {t} _2 $ groups及其在残留类中的行为的普通zeta功能
Normal zeta functions of small $\mathfrak{T}_2$-groups and their behaviour on residue classes
论文作者
论文摘要
令$ g $成为有限生成的Nilpotent-2类无扭转组。我们研究ZETA函数如何列举G的正常亚组在残基类别上有所不同。特别是，我们表明，对于小于或等于7的小$ g $的hirsch长度，普通的zeta函数通常在残基类别上始终是理性的功能。然后，我们证明有hirsch长度8的组的示例，其正常Zeta函数不是残基类别的合理函数。我们观察到与希格曼的猪猜想的联系。
Let $G$ be a finitely generate nilpotent class-2 torsion-free group. We study how the zeta function enumerating normal subgroups of G varies on residue classes. In particular, we show that for small such $G$ of Hirsch length less than or equal to 7, the normal zeta functions are generically always rational functions on residue classes. We then show that there are examples of groups with Hirsch length 8 whose normal zeta function is not a rational function on residue classes. We observe the connection to Higman's PORC conjecture.
