Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nilpotency in automorphic loops of prime power order   A loop is automorphic if its inner mappings are automorphisms. Using
so-called associated operations, we show that every commutative automorphic
loop of odd prime power order is centrally nilpotent. Starting with anisotropic
planes in the vector space of $2\times 2$ matrices over the field of prime
order $p$, we construct a family of automorphic loops of order $p^3$ with
trivial center.

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The categories of this paper are: stat
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The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: hep-lat