Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Not all finitely generated groups have universal acylindrical actions   The class of acylindrically hyperbolic groups, which are groups that admit a
certain type of non-elementary action on a hyperbolic space, contains many
interesting groups such as non-exceptional mapping class groups and
$\operatorname{Out}(\mathbb F_n)$ for $n\geq 2$. In such a group, a generalized
loxodromic element is one that is loxodromic for some acylindrical action of
the group on a hyperbolic space. Osin asks whether every finitely generated
group has an acylindrical action on a hyperbolic space for which all
generalized loxodromic elements are loxodromic. We answer this question in the
negative, using Dunwoody's example of an inaccessible group as a
counterexample.

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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
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The categories of this paper are: chao-dyn
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The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
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The categories of this paper are: econ
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: quant-ph