Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Commutation Semigroups of Dihedral Groups   For G a group and g in G, we define mappings pg(G) and lg(G) from G into G by
pg(x)=[x,g] and lg(x)=[g,x]. We let P(G) and L(G) denote the subsemigroups of
the set of all mappings from G to G generated by {pg: g in G} and {lg: g in G},
respectively. P(G) and L(G) are called the right and left commutation semigroup
of G, respectively. In this paper we will give explicit formulas for the orders
of both P(G) and L(G) where G is a dihedral group.

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The categories of this paper are: hep-th
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: atom-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: chao-dyn
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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: cond-mat
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The categories of this paper are: acc-phys