Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Approximate subloops and Freiman's theorem in finitely generated
  commutative moufang loops   Fix a parameter $K\geqslant 1$. A $K$-approximate subgroup is a finite set
$A$ in a group $G$ which contains the identity, is symmetric and such that
$A.A$ can covered by $K$ left translates of $A$. This article deals with the
generalisation of the concept of approximate groups in the case of loops which
we call approximate loops and the description of $K$-approximate subloops when
the ambient loop is a finitely generated commutative moufang loop. Specifically
we have a Freiman type theorem where such approximate subloops are controlled
by arithmetic progressions defined in the commutative moufang loops.

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The categories of this paper are: cond-mat
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The categories of this paper are: alg-geom
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: acc-phys
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The categories of this paper are: funct-an
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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: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: eess
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The categories of this paper are: patt-sol