Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal zeta functions of small $\mathfrak{T}_2$-groups and their
  behaviour on residue classes   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.

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The categories of this paper are: math-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: cs
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The categories of this paper are: astro-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con