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

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


研究成果: 雜誌貢獻期刊論文同行評審

8 引文 斯高帕斯(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.

頁(從 - 到)483-492
期刊Journal of Algebra and its Applications
出版狀態已發佈 - 2010 6月

ASJC Scopus subject areas

  • 代數與數理論
  • 應用數學


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