Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Decomposing p-groups via Jordan algebras   For finite p-groups P of class 2 and exponent p the following are invariants
of fully refined central decompositions of P: the number of members in the
decomposition, the multiset of orders of the members, and the multiset of
orders of their centers. Unlike for direct product decompositions, Aut P is not
always transitive on the set of fully refined central decompositions, and the
number of orbits can in fact be any positive integer. The proofs use the
standard semi-simple and radical structure of Jordan algebras. These algebras
also produce useful criteria for a p-group to be centrally indecomposable.

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The categories of this paper are: patt-sol
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: q-alg
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: hep-ex
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The categories of this paper are: physics
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The categories of this paper are: gr-qc