Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Groups in which Squares and Cubes Commute   If for all $a, b$ in a group $G$, we have that $a^2b^2 = b^2a^2$ and $a^3b^3
= b^3a^3$ then does the group necessarily have to be abelian? This paper shows
that the answer is affirmative for finite groups as well as certain classes of
infinite groups. In general we show that if $G$ is an infinite group in which
squares commute and cubes commute then the set of torsion elements of $G$
denoted by $T(G)$ has to be an abelian normal subgroup of $G$.

22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
9
The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: plasm-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
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The categories of this paper are: acc-phys