Multiplicative Jordan decomposition in group rings of 3-groups

Chia Hsin Liu*, D. S. Passman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


In this paper, we essentially classify those finite 3-groups G having integral group rings with the multiplicative Jordan decomposition property. If G is abelian, then it is clear that ℤ[G] satisfies MJD. Thus, we are only concerned with the nonabelian case. Here we show that ℤ[G] has the MJD property for the two nonabelian groups of order 33. Furthermore, we show that there are at most three other specific nonabelian groups, all of order 34, with ℤ[G] having the MJD property. Unfortunately, we are unable to decide which, if any, of these three satisfies the appropriate condition.

Original languageEnglish
Pages (from-to)505-519
Number of pages15
JournalJournal of Algebra and its Applications
Issue number4
Publication statusPublished - 2009


  • 3-group
  • Integral group ring
  • Multiplicative Jordan decomposition

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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