Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Embedding Groups into Distributive Subsets of the Monoid of Binary
  Operations   Let X be a set and Bin(X) the set of all binary operations on X. We say that
a subset of Bin(X) is a distributive set of operations if all pairs of elements
are right distributive. J.Przytycki posed the question of which groups can be
realized as distributive sets. The initial guess that any group may be embedded
into Bin(X) for some X was complicated by an observation that if a binary
operation is idempotent (a*a=a), then it commutes with every element of S. The
first noncommutative subgroup of Bin(X), the symmetric group on three elements,
was found in October of 2011 by Y.Berman. We show that any group can be
embedded in Bin(X) for X=G (as a set). We also discuss minimality of embeddings
observing that, in particular, X with six elements is the smallest set such
that Bin(X) contains a non-abelian subgroup.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat