Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Detecting a subclass of torsion-generated groups   We classify the groups quasi-isometric to a group generated by finite-order
elements within the class of one-ended hyperbolic groups which are not Fuchsian
and whose JSJ decomposition over two-ended subgroups does not contain rigid
vertex groups. To do this, we characterize which JSJ trees of a group in this
class admit a cocompact group action with quotient a tree. The conditions are
stated in terms of two graphs we associate to the degree refinement of a group
in this class. We prove there is a group in this class which is quasi-isometric
to a Coxeter group but is not abstractly commensurable to a group generated by
finite-order elements. Consequently, the subclass of groups in this class
generated by finite-order elements is not quasi-isometrically rigid. We provide
necessary conditions for two groups in this class to be abstractly
commensurable. We use these conditions to prove there are infinitely many
abstract commensurability classes within each quasi-isometry class within this
class that contains a group generated by finite-order elements.

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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-th
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys