Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On abstract commensurators of surface groups   Let $\Gamma$ be the fundamental group of a surface of finite type and
Comm$(\Gamma)$ be its abstract commensurator. Then Comm$(\Gamma)$ contains the
solvable Baumslag--Solitar groups $\langle a ,b : a b a^{-1} = b^n \rangle$ for
any $n > 1$. Moreover, the Baumslag--Solitar group $\langle a ,b : a b^2 a^{-1}
= b^3 \rangle$ has an image in Comm$(\Gamma)$ that is not residually finite.
Our proofs are computer-assisted. Our results also illustrate that
finitely-generated subgroups of Comm$(\Gamma)$ are concrete objects amenable to
computational methods. For example, we give a proof that $\langle a ,b : a b^2
a^{-1} = b^3 \rangle$ is not residually finite without the use of normal forms
of HNN extensions.

31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
18
The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas