Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A note on factorizations of finite groups   In Question 19.35 of the Kourovka Notebook, M. H. Hooshmand asks whether,
given a finite group $G$ and a factorization $\mathrm{card}(G)= n_1\ldots n_k$,
one can always find subsets $A_1,\ldots,A_k$ of $G$ with
$\mathrm{card}(A_i)=n_i$ such that $G=A_1\ldots A_k;$ equivalently, such that
the group multiplication map $A_1\times\ldots\times A_k\to G$ is a bijection.
  We show that for $G$ the alternating group on 4 elements, $k=3$, and
$(n_1,n_2,n_3) = (2,3,2)$, the answer is negative. We then generalize some of
the tools used in our proof, and note an open question.

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The categories of this paper are: stat
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
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The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
19
The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
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: ao-sci
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The categories of this paper are: cmp-lg