Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Noncommutative sets of small doubling   A corollary of Kneser's theorem, one sees that any finite non-empty subset
$A$ of an abelian group $G = (G,+)$ with $|A + A| \leq (2-\eps) |A|$ can be
covered by at most $\frac{2}{\eps}-1$ translates of a finite group $H$ of
cardinality at most $(2-\eps)|A|$. Using some arguments of Hamidoune, we
establish an analogue in the noncommutative setting. Namely, if $A$ is a finite
non-empty subset of a nonabelian group $G = (G,\cdot)$ such that $|A \cdot A|
\leq (2-\eps) |A|$, then $A$ is either contained in a right-coset of a finite
group $H$ of cardinality at most $\frac{2}{\eps}|A|$, or can be covered by at
most $\frac{2}{\eps}-1$ right-cosets of a finite group $H$ of cardinality at
most $|A|$. We also note some connections with some recent work of Sanders and
of Petridis.

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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: nucl-ex
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The categories of this paper are: chem-ph
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: stat
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The categories of this paper are: physics
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: dg-ga