Multiplicative jordan decomposition in group rings of 2, 3-groups

Chia Hsin Liu*, D. S. Passman, T. Y. Lam

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


In this paper, we essentially finish the classification of those finite 2, 3-groups G having integral group rings with the multiplicative Jordan decomposition (MJD) property. If G is abelian or a Hamiltonian 2-group, then it is clear that ℤ[G] satisfies MJD. Thus, we need only consider the nonabelian case. Recall that the 2-groups with MJD were completely determined by Hales, Passi and Wilson, while the corresponding 3-groups were almost completely determined by the present authors. Thus, we are concerned here, for the most part, with groups whose order is divisible by 6. As it turns out, there are precisely three nonabelian 2, 3-groups, of order divisible by 6, with ℤ[G] satisfying MJD. These have orders 6, 12, and 24. In view of another result of Hales, Passi and Wilson, this completes a significant portion of the classification of all finite groups with MJD.

Original languageEnglish
Pages (from-to)483-492
Number of pages10
JournalJournal of Algebra and its Applications
Issue number3
Publication statusPublished - 2010 Jun


  • 2,3-group
  • Integral group ring
  • multiplicative Jordan decomposition

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics


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