Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Residual properties of graph products of groups   We prove that the class of residually C groups is closed under taking graph
products, provided that C is closed under taking subgroups, finite direct
products and that free-by-C groups are residually C. As a consequence, we show
that local embeddability into various classes of groups is stable under graph
products. In particular, we prove that graph products of residually amenable
groups are residually amenable, and that locally embeddable into amenable
groups are closed under taking graph products.

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The categories of this paper are: nlin
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The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: chao-dyn
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The categories of this paper are: econ
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The categories of this paper are: solv-int