Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local commensurability graphs of solvable groups   The commensurability index between two subgroups $A, B$ of a group $G$ is $[A
: A \cap B] [B : A\cap B]$. This gives a notion of distance amongst
finite-index subgroups of $G$, which is encoded in the p-local commensurability
graphs of $G$. We show that for any metabelian group, any component of the
$p$-local commensurabilty graph of $G$ has diameter bounded above by 4.
However, no universal upper bound on diameters of components exists for the
class of finite solvable groups. In the appendix we give a complete
classification of components for upper triangular matrix groups in
$\text{GL}(2, \mathbb{F}_q)$.

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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
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The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: stat
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: econ