Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Classification of the virtually cyclic subgroups of the pure braid
  groups of the projective plane   We classify the (finite and infinite) virtually cyclic subgroups of the pure
braid groups $P_{n}(RP^2)$ of the projective plane. The maximal finite
subgroups of $P_{n}(RP^2)$ are isomorphic to the quaternion group of order 8 if
$n=3$, and to $\Z_{4}$ if $n\geq 4$. Further, for all $n\geq 3$, up to
isomorphism, the following groups are the infinite virtually cyclic subgroups
of $P_{n}(RP^2)$: $\Z$, $\Z_{2} \times \Z$ and the amalgamated product $\Z_{4}
\ast_{\Z_{2}} \Z_{4}$.

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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: stat
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The categories of this paper are: supr-con
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The categories of this paper are: dg-ga
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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: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas