In this paper, we complete the classification of those finite 3-groups G whose integral group rings have the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies the multiplicative Jordan decomposition (1) MJD. In the nonabelian case, we show that ℤ[G] satisfies MJD if and only if G is one of the two nonabelian groups of order 33 = 27.
- Integral group ring
- Multiplicative Jordan decomposition
ASJC Scopus subject areas
- Algebra and Number Theory