Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nilpotent Decomposition in Integral Group Rings   A finite group $G$ is said to have the nilpotent decomposition property (ND)
if for every nilpotent element $\alpha$ of the integral group ring
$\mathbb{Z}[G]$ one has that $\alpha e$ also belong to $\mathbb{Z}[G]$, for
every primitive central idempotent $e$ of the rational group algebra
$\mathbb{Q}[G]$. Results of Hales, Passi and Wilson, Liu and Passman show that
this property is fundamental in the investigations of the multiplicative Jordan
decomposition of integral group rings. If $G$ and all its subgroups have ND
then Liu and Passman showed that $G$ has property SSN, that is, for subgroups
$H$, $Y$ and $N$ of $G$, if $N\lhd H $ and $Y\subseteq H$ then $N\subseteq Y$
or $YN$ is normal in $H$; and such groups have been described. In this article,
we study the nilpotent decomposition property in integral group rings and we
classify finite SSN groups $G$ such that the rational group algebra
$\mathbb{Q}[G]$ has only one Wedderburn component which is not a division ring.

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The categories of this paper are: hep-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: eess
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom