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Nilpotent Decomposition in Integral Group Rings
A finite group is said to have the nilpotent decomposition property (ND)
if for every nilpotent element of the integral group ring
one has that also belong to , for
every primitive central idempotent of the rational group algebra
. 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 and all its subgroups have ND
then Liu and Passman showed that has property SSN, that is, for subgroups
, and of , if and then
or is normal in ; 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 such that the rational group algebra
has only one Wedderburn component which is not a division ring.Comment: This paper is to appear in Journal of Algebr
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