Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The p-width of the alternating groups   Let $p$ be a fixed prime. For a finite group generated by elements of order
$p$, the $p$-width is defined to be the minimal $k\in\mathbb{N}$ such that any
group element can be written as a product of at most $k$ elements of order $p$.
Let $A_{n}$ denote the alternating group of even permutations on $n$ letters.
We show that the $p$-width of $A_{n}$ $(n\geq p)$ is at most $3$. This result
is sharp, as there are families of alternating groups with $p$-width precisely
3, for each prime $p$.

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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
4
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: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph