Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The IA-congruence kernel of high rank free Metabelian groups   The congruence subgroup problem for a finitely generated group $\Gamma$ and
$G\leq Aut(\Gamma)$ asks whether the map $\hat{G}\to Aut(\hat{\Gamma})$ is
injective, or more generally, what is its kernel $C\left(G,\Gamma\right)$? Here
$\hat{X}$ denotes the profinite completion of $X$. In this paper we investigate
$C\left(IA(\Phi_{n}),\Phi_{n}\right)$, where $\Phi_{n}$ is a free metabelian
group on $n\geq4$ generators, and $IA(\Phi_{n})=\ker(Aut(\Phi_{n})\to
GL_{n}(\mathbb{Z}))$.
  We show that in this case $C(IA(\Phi_{n}),\Phi_{n})$ is abelian, but not
trivial, and not even finitely generated. This behavior is very different from
what happens for free metabelian group on $n=2,3$ generators, or for finitely
generated nilpotent groups.

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The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
28
The categories of this paper are: alg-geom
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: comp-gas