Article ID Journal Published Year Pages File Type
4585268 Journal of Algebra 2013 16 Pages PDF
Abstract

If G   is a finite group whose integral group ring Z[G]Z[G] has the multiplicative Jordan decomposition property, then it is known that all Wedderburn components of the rational group ring Q[G]Q[G] have degree at most 3. While degree 3 components can occur, we prove here that if they do, then certain central units in Z[G]Z[G] cannot exist. With this, we are able to greatly simplify the argument that characterizes those 3-groups with integral group ring having MJD. Furthermore, we show that if G   is a nonabelian semidirect product of the form Cp⋊C3kCp⋊C3k, with prime p>7p>7 and with the cyclic 3-group acting like a group of order 3, then Z[G]Z[G] does not have MJD.

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Related Topics
Physical Sciences and Engineering Mathematics Algebra and Number Theory
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