Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Certain residual properties of generalized Baumslag-Solitar groups   Let $G$ be a generalized Baumslag-Solitar group and $\mathcal{C}$ be a class
of groups containing at least one non-unit group and closed under taking
subgroups, extensions, and Cartesian products of the form $\prod_{y \in
Y}X_{y}$, where $X, Y \in \mathcal{C}$ and $X_{y}$ is an isomorphic copy of $X$
for every $y \in Y$. We give a criterion for $G$ to be residually a
$\mathcal{C}$-group provided $\mathcal{C}$ consists only of periodic groups. We
also prove that $G$ is residually a torsion-free $\mathcal{C}$-group if
$\mathcal{C}$ contains at least one non-periodic group and is closed under
taking homomorphic images. These statements generalize and strengthen some
known results. Using the first of them, we provide criteria for a GBS-group to
be a) residually nilpotent; b) residually torsion-free nilpotent; c) residually
free.

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The categories of this paper are: adap-org
9
The categories of this paper are: nlin
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The categories of this paper are: solv-int
8
The categories of this paper are: hep-ex
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The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: physics
34
The categories of this paper are: chem-ph